bluuebunny/crossref_metadata_2025 huggingface dataset:
Setchellanthaceae (Capparales), a new family for a relictual, glucosinolate‐producing endemic of the Mexican deserts
Authors: Iltis Hugh H.
Published: April 2006

Iltis, H. H.: Setchellanthaceae (Capparales), a new family for a relictual, glucosinolate‐producing endemic of the Mexican deserts. – Taxon 48: 257‐275. 1999. – ISSN 0040‐0262.

Setchellanthus caeruleus Brandegee is a rare microphyllous shrub, densely pubescent with T‐shaped Malpighian hairs, with many stamens, 5‐7 free blue to lilac petals, an elongate, 3‐carpellate, deeply trisulcate ovary with axile placentation and proto‐parietal vasculature, and a straight embryo essentially lacking endosperm. It is known only from two widely disjunct areas in the Chihuahuan and Tehuacán deserts of northern and south‐central Mexico. The genus was named for phycologist W. A. Setchell (1864‐1963; a biographical note is included). Its taxonomy, morphology, and geography are outlined, and the results of four associated papers on flower and seed anatomy, vegetative anatomy, pollen structure, and nucleotide sequence of the rbcL gene are discussed. The species is so highly distinct in its relatively primitive morphology and chemistry that it is here placed into its own, newly established monotypic family near the Caricaceae and Moringaceae and basal to the core group of glucosinolate (mustard oil) producing families (but less basal than, e.g., Bretschneideraceae, Akaniaceae, and Tropaeolaceae). The new evidence supports Dahlgren's reclassification of an expanded order Capparales.
Botanical libraries and herbaria in North America. 2. The Rudolph natural history library and its acquisition by the Ohio State University
Authors: Stuessy Tod F. , Stuckey Ronald L. , Boomgaarden Wesley L. , Burk William R.
Published: April 2006

Stuessy, T. F., Stuckey, R. L., Boomgaarden, W. L. & Burk, W. R.: Botanical libraries and herbaria in North America. 2. The Rudolph natural history library and its acquisition by the Ohio State University. – Taxon 46: 643‐648.1997. – ISSN 0040‐0262.

Emanuel D. Rudolph, professor of botany at the Ohio State University and his wife, Ann Waterman Rudolph, developed a large personal natural history library totalling more than 53,000 volumes. Their entire library was willed to the Ohio State University, with approximately 11,000 botanical volumes donated to the Herbarium Library. These books mostly represent subjects in biogeography, biography, cryptogamic botany (especially lichenology), economic botany, general botany, and history of botany. Prominent authors are Acharius, Amos Eaton, Almira Lincoln Phelps, Lindley, Linnaeus, Ray, Schleiden, and Alphonso Wood. Holdings extend back to the 16th century.
Botanical libraries and herbaria in North America. 4. The Samuel Botsford Buckley – Rebecca Mann Dean mystery
Authors: Dorr Laurence J.
Published: April 2006

Dorr, L. J.: Botanical libraries and herbaria in North America. 4. The Samuel Botsford Buckley – Rebecca Mann Dean mystery. – Taxon 46: 661‐687. 1997. – ISSN 0040‐0262.

Samuel Botsford Buckley (1809‐1884) amassed a herbarium of approximately 6000 specimens through his own labours and through exchange with other botanists, mostly American but also European. This herbarium was acquired by Rebecca Mann Dean (1821‐1890), a professor of natural history and other subjects at Antioch College, Yellow Springs, Ohio, and wife of a bookstore owner who had a brief row with Buckley in the 1850s. Before her death, she sold Buckley's herbarium to Washington University, St Louis, Missouri. Within a few years of the sale, the herbarium was combined with that of the Missouri Botanical Garden. Neither the botanical activities of Buckley, which are fairly well understood, nor the nature of the transaction conveying the herbarium from Buckley to Dean, which is still problematic, could have been sketched without information contained in correspondence saved by botanical libraries and other scholarly institutions. The importance of keeping botanical libraries and archives in close proximity to herbaria is reaffirmed by this case study.
In defense of Latin for describing new taxa
Authors: Filgueiras Tarciso S.
Published: April 2006

Filgueiras, T. S.: In defense of Latin for describing new taxa. – Taxon 46: 747‐749. 1997. – ISSN 0040‐0262.

Latin should remain mandatory for describing new taxa. The optional use of English under the proposed BioCode is unacceptable. Whereas the English language is the expression of certain living cultures, a certain political and economic system, Latin belongs to no single nation and yet it belongs to all. Latin is a patrimony of humanity.
New evidence for the systematic position of Gundelia L. with notes on delimitation of Arctoteae (Asteraceae)
Authors: Karis Per Ola , Eldenäs Pia , Källersjö Mari
Published: April 2006

Karis, P. O., Eldenäs, P. & Källersjö, M.: New evidence for the systematic position of Gundelia L. with notes on delimitation of Arctoteae (Asteraceae). – Taxon 50: 105–114. 2001. – ISSN 0040‐0262.

The systematic position of the thistle‐like Gundelia of Asteraceae‐Arctoteae is investigated by using sequences from the chloroplast gene ndhF in a parsimony jackknife analysis. Unexpectedly, the analysis indicates strong support for placing Gundelia with tribe Lactuceae, rather than with tribe Arctoteae. Gundelia's morphology is discussed in light of this new grouping. Another clade, although weakly supported, is formed by representatives of Arctoteae, including the two South African genera Eremothamnus and Hoplophyllum. The latter two form a sister group with 100 % support.
Lectotypification of Pinus mugo Turra (Pinaceae)
Authors: Minghetti Paolo , Nardi Enio
Published: April 2006

Minghetti, P. & Nardi, E.: Lectotypification of Pinus mugo Turra (Pinaceae). – Taxon 48: 465‐469. 1999. – ISSN 0040‐0262.

The lectotype of Pinus mugo from the Séguier Herbarium, designated here, belongs to introgressive populations between the eastern and the western subspecies, generally named P. mugo subsp. mugo and subsp. uncinata, respectively. The name P. mugo subsp. mugo would not therefore represent the eastern populations of the species, as has been generally accepted, but should be adopted for the central, intermediate subspecies, known to date as P. mugo subsp. rotundata. This change, however, would so much disrupt the established nomenclature of the group that it is advisable to conserve the name P. mugo with a type that agrees with current usage.
Report of the Committee for Fungi: 6
Authors: Gams Walter
Published: April 2006

Gams, W.: Report of the Committee for Fungi: 6. – Taxon 45: 309‐311. 1996. – ISSN 0040‐0262.

The Committee for Fungi reports its recommendations on 36 proposals to conserve or reject names, recommending 35.
On Cyrtolejeunea A. Evans (Lejeuneaceae, Hepaticae)
Authors: Grolle Riclef , Zhu Rui‐Liang , Gradstein S. Rob
Published: April 2006

Grolle, R., Zhu, R.‐L. & Gradstein, S. R.: On Cyrtolejeunea A.Evans (Lejeuneaceae, Hepaticae). ‐ Taxon 50: 1067–1074. 2001. ‐ ISSN 0040–0262.

The liverwort genus Cyrtolejeunea A. Evans is reduced to synonymy under Cheilolejeunea (Spruce) Schiffn. because of the existence of a series of intermediate species, including Cheilolejeunea insecto Grolle & Gradst. sp. nov. from Bolivia and Brazil and Cheilolejeunea chenii R.L. Zhu & M.L. So from eastern China. The new combinations, Cheilolejeunea holostipa (Spruce) Grolle & R.L. Zhu comb. nov. and C. suzannensis (Grolle) Grolle & R.L. Zhu comb, nov., are proposed.
Lectotypifications and neotypifications in Lantana and Lippia (Verbenaceae)
Authors: Silva Tânia Regina dos Santos
Published: April 2006

dos Santos Silva, T. R.: Lectotypifications and neotypifications in Lantana and Lippia (Verbenaceae). – Taxon 50: 1115–1118. 2001. ‐ ISSN 0040–0262.

In preparing a revision of the genera Lantana L. and Lippia L. in Brazil, 19 species names and 1 varietal name were found to require typification. These are typified in the present paper, 17 by lectotypes and three by neotypes.
On the nomenclatural status of the morphogenera, Quereuxia and Trapago
Authors: Hickey Leo J.
Published: April 2006

Hickey, L. J.: On the nomenclatural status of the morphogenera, Quereuxia and Trapago. – Taxon 50: 1119–1124. 2001. ‐ ISSN 0040–0262.

Quereuxia Krysht. ex Baikovskaja is the correct name for a morphogenus of leaves and leaf rosettes belonging to an aquatic angiosperm of Late Cretaceous to Palaeocene age in North America and Eurasia and must be accepted instead of its illegitimate junior synonym, Trapago McIver & Basinger. In addition, the name Jonquieria Krassilov, though based on a separate type, falls well within the circumscription of Quereuxia and is here regarded as another later synonym, which requires the new combination Quereuxia vachrameevii (Krassilov) L.J. Hickey.
Typification of Echinacea purpurea (L.) Moench (Heliantheae: Asteraceae) and its implications for the correct naming of two Echinacea taxa
Authors: Binns Shannon E. , Baum Bernard R. , Arnason John T.
Published: April 2006

Binns, S. E., Baum, B. R., & Arnason, J. T.: Typification of Echinacea purpurea (L.) Moench (Heliantheae: Asteraceae) and its implications for the correct naming of two Echinacea taxa. – Taxon 50: 1169–1175. 2001. ‐ ISSN 0040–0262.

A thorough investigation of relevant nomenclatural types and descriptions reveals that the name Echinacea purpurea (L.) Moench, which was lectotypified by McGregor in 1968, has been consistently misapplied since 1903 to a taxon distinctly different from that of its modern lectotype and of the original Linnaean concept. Linnaeus's original concept of Rudbeckia purpurea, maintained by Candolle as Echinacea purpurea when he segregated E. serótina (Nutt.) DC., is the species now known as E. laevigata (C. L. Boynton & Beadle) S. F. Blake. Technically, therefore, the correct name for the species currently called E. laevigata is E. purpurea (L.) Moench, and the correct name for the species currently called E. purpurea is E. serotina (Nutt.) DC., for which a lectotype is designated. Conservation of the name E. purpurea in the sense of its current application, which also preserves the usage of E. laevigata, is proposed in a separate article (see Binns & al., p. 1199, this issue).
A new tribal classification of Mesembryanthemaceae: evidence from floral nectaries
Authors: Chesselet Pascale , Smith Gideon F. , van Wyk Abraham E.
Published: April 2006

Mesembryanthemaceae Fenzl, here defined as excluding Aizoaceae Rudolphi s.str., are divided into five major groups, primarily on the basis of characters of the floral nectary. In terms of nectary type, the meronectary is considered a synapomorphy for the family Mesembryanthemaceae. The koilomorphic meronectary is a synapomorphy for subfamily Mesembryanthemoideae, considered the basal group; it is not further divided at tribal level. Four distinct nectary types characterize the more specialized subfamily Ruschioideae Schwantes in Ihlenf., Schwantes & Straka emend. Bittrich & H.E.K. Hartmann, and are used here to establish a new tribal classification for the group. Tribe Apatesieae Schwantes emend. Chesselet, G.F. Sm. & A.E. van Wyk (seven genera) is characterized by a broad, flat holonectary. Fruits in this tribe have diversified and several have lost hygrochastic properties. The group is regarded as primitive among Ruschioideae. Subtribe Dorotheanthinae Schwantes ex Ihlenf. & Struck (three genera) is raised to tribal level as Dorotheantheae (Schwantes ex Ihlenf. & Struck) Chesselet, G.F. Sm. & A.E. van Wyk. Plants in this tribe have semi‐succulent leaves and all are annuals. The group has flowers with broad, flat meronectaries, and is not defined by any synapomorphy in terms of nectary type. Tribe Delospermeae Chesselet, G.F. Sm. & A.E. van Wyk (27 genera) is newly proposed to include all taxa with a lophomorphic meronectary; it has diversified mostly in the summer‐rainfall region of southern Africa. Tribe Ruschieae, as emended here, incorporates 71 genera. It is characterized by a lophomorphic holonectary and has diversified mostly in the arid winter‐rainfall region of southern Africa. Nectary types suggest primitiveness of Delospermeae in relation to Ruschieae among the highly succulent ruschioid taxa and support previous hypotheses suggesting that more derived Ruschioideae originated in the summer‐rainfall region of southern Africa.
Circumscription, classification, and (Bryopsida) inferred from nuclear and chloroplast DNA sequence data and morphology taxonomy of Amblystegiaceae
Authors: Vanderpoorten Alain , Hedenäs Lars , Cox Cymon J. , Shaw A. Jonathan
Published: April 2006

Results from a previous broad­scale analysis employing trnL­trnF sequence data for 168 Hypnalean and 11 Hookerialean taxa, and an analysis employing two chloroplast regions, trnL­trnF and atpB­rbcL, one nuclear region, the internal transcribed spacers of 18S­26S rDNA, plus 68 morphological characters for a reduced data set of 54 Hypnalean taxa, were used to circumscribe Amblystegiaceae. The analyses provided two well­supported main clades including taxa traditionally included in Amblystegiaceae s.l. and recognized as Amblystegiaceae s.str. [Anacamptodon, Amblystegium, Campyliadelphus, Campylium, Cratoneuron, Cratoneuropsis, Drepanocladus s.str., Gradsteinia, Hygrohypnum s.str. (including the type species, H. luridum, but excluding a number of other species previously accommodated in the genus), Hypnobartlettia, Leptodictyum, Palustriella, Pseudo­calliergon, and Serpoleskea] and Calliergonaceae stat. nov. (Calliergon, Hamatocaulis, Loeskypnum, Straminergon, and Warnstorfia). Scorpidium and "Hygrohypnum" ochraceum were closely related to Calliergonaceae but were not included in the family because of the lack of support. All these genera but Anacamptodon have previously been included in Amblystegiaceae s.l. The sporophytic features of Anacamptodon, which contrast with those of all the other members of Amblystegiaceae, are interpreted as adaptations to an epiphytic habitat and suggest, together with other recent taxonomic works in Hookeriales, that characters related to sporophytic specializations are among the most homoplastic. Several other taxa (Calliergonella, Campylophyllum, Conardia, Donrichardsia, "Hygrohypnum" smithii, Platydictya, Sanionia), previously included in Amblystegiaceae s.l., appeared more closely related to other Hypnalean families. Recircumscribed Amblystegiaceae, and several clades within the family, have no identifiable morphological synapomorphies. A new system of classification for recircumscribed Amblystegiaceae, including morphological delimitation of presented clades based on maximum likelihood reconstruction of ancestral character states, is proposed and appropriate nomenclatural changes made.
Precision and Parsimony
Authors: Williams David M.
Published: April 2006

The effects of standard parsimony and three­item statement analysis, two different approaches to cladistics, are examined relative to a series of matrices where plesiomorphic values in one taxon are increased in a regular fashion. Analyses of these matrices suggest that standard parsimony is less sensitive to these changes than three­item statement analysis.
Revised typification of Veronica agrestis L. (Scrophulariaceae)
Authors: Martínez-Ortega Maria Montserrat , Sánchez José Ángel , Cafferty Steve , Rico Enrique , Thulin Mats
Published: April 2006

A previously designated lectotype for the name Veronica agrestis L. is here superseded in favour of an alternative original element on the grounds of conflict with the protologue in accordance with Art. 9.17(b) of the International Code of Botanical Nomenclature. An earlier proposal to conserve the name with a conserved type is withdrawn.
Neotypification of Uvaria hirsuta Jack (Annonaceae)
Authors: Meade Conor V. , Parnell John A. N.
Published: April 2006

Uvaria hirsuta Jack is one of the more common species of the genus Uvaria (Annonaceae) in the Malay Peninsula and Sumatra. The original type was destroyed in 1824, and any duplicates which may have existed are now lost. Wallich Herbarium Catalogue no. 6458b is proposed here as neotype for U. hirsuta. The specimen is of high quality, includes both flowers and fruits, and was collected at the type locality soon after Jack’s original collections.
Designation of an epitype for Helotium yunnanense and its transfer to the genus Lambertella (Rutstroemiaceae, Ascomycota)
Authors: Zhuang Wen-Ying , Zhang Yan-Hui
Published: April 2006

Helotium yunnanense is re‐described based upon examination of the holotype and an epitype designated, due to the lack of apothecia matching the original description in the holotype material. Detailed morphological study indicated that the fungus is a member of the genus Lambertella. A new combination, Lambertella yunnanensis, is, therefore, proposed.
On the typification of two misunderstood Roccella (Lichenized fungi) names, R. tinctoria and R. fucoides
Authors: Tehler Anders
Published: April 2006

The nomenclature and taxonomy of two Roccella species are examined and clarified. Roccella tinctoria DC., a nomen novum for Lichen roccella L., replaces Roccella vincentina [“vicentina”] (Vain.) Follm., the name which has been most commonly used in recent years for this sorediate species. Roccella fucoides (Dicks.) Vain, based on Lichen fucoides Dicks., is neotypified and is the correct name for what has been known as R. phycopsis, now shown to be an illegitimate superfluous name for R. fucoides.
Superimposed non-stationary renewal processes
Authors: Blumenthal S. , Greenwood J. A. , Herbach L.
Published: April 2006

For superposition of independent, stationary renewal processes, it is well known that the distribution of waiting time between events for the superimposed process is approximately exponential if the number of processes involved is sufficiently large, (see Khintchine (1960), Ososkov (1956)). We assume that all component processes have the same age t, and we generalize the classical result to show that even for t finite (non-stationary case), the limiting waiting time distribution (as the number of processes increases) is exponential with a scale parameter which depends on t through the average of the individual process renewal densities.
The progeny of a branching process
Authors: Doney R. A.
Published: April 2006

1. Let {Z(t), t ≧ 0} be an age-dependent branching process with offspring generating function and life-time distribution function G(t). Denote by N(t) the progeny of the process, that is the total number of objects which have been born in [0, t], counting the ancestor. (See Section 2 for definitions.) Then in the Galton-Watson process (i.e., when G(t) = 0 for t ≦ 1, G(t) = 1 for t > 1) we have the simple relation Nn = Z0 + Z1 + ··· + Zn, so that the asymptotic behaviour of Nn as n → ∞ follows from a knowledge of the asymptotic behaviour of Zn. In particular, if 1 < m = h'(1) < ∞ and Zn(ω)/E(Zn) → Z(ω) > 0 then also Nn(ω)/E(Nn) → Z(ω) > 0; since E(Zn)/E(Nn) → 1 – m–1 this means that
Occupation times of stationary gaussian processes
Authors: Berman Simeon M.
Published: April 2006

Let X(t), t ≧ 0, be a stationary Gaussian process with zero mean, unit variance and continuous covariance function r(t). Suppose that, for some ε > 0
so that there is a version of the process whose sample functions are continuous [1].
Identifiability in GI/G/k queues
Authors: Ross Sheldon M.
Published: April 2006

Consider a queueing system in which customers arrive in accordance with a renewal process having an interarrival distribution F, and in which the service times of customers are independent and have distribution G. Moreover, suppose that there are k (k ≦ ∞) servers and that an arriving customer is immediately served if he finds one of the servers free, and if not then he joins the queue.
The proportions of individuals of different kinds in two-type populations. A branching process problem arising in biology
Authors: Jagers P.
Published: April 2006

Consider an age-dependent branching process with two types of individuals. Suppose that individuals of one type beget children of both types, whereas those of the other type can only give birth to individuals of their own kind. This paper is a study of the relation between two random functions occurring in such processes starting from an ancestor of the first type, the two functions being the numbers of individuals of the two kinds. Under weak assumptions it is shown that the random proportion of individuals of one type converges as time passes, in mean square as well as almost surely to a non-random limit, easily determined in terms of the reproduction laws and life-length distributions of the process.
Used item replacement policy
Authors: Bhat B.R.
Published: April 2006

The block replacement policy, wherein items are replaced at regular intervals of time and on failure, is rather wasteful because sometimes almost new items are also removed. As an alternative a policy of replacement by new items at regular intervals of time and by used items on failure, is suggested. The consequences of this policy, called used item replacement policy, are studied for Erlangian and sub-exponential life-time distributions. The latter distribution which is the difference of two negative exponential distributions, does not seem to have received much attention in the literature so far.
Statistical relativistic particle
Authors: Gilson J. G.
Published: April 2006

This paper arises from the observation by Dirac [1] that an exact measurement of the velocity of an electron should give one of the instantaneous values ± c. The velocity v < c with which the electron moves bodily is in some statistical sense an average. This aspect of the quantum states of motion of a relativistic particle has frequently been mentioned [2], [3] and, as is wellknown, is connected with the self energy problem. Such deductions from quantum mechanics have led the author to consider the possibility of constructing from purely statistical ideas an entity having the physical properties of a relativistic elementary particle. One might reasonably hope to build up characteristics such as rest mass and spin in such a scheme. Properties such as energy and momentum will arise as averages over fluctuating random quantities. In this paper we shall concentrate on rest mass, energy and momentum. We shall show that a zero rest mass object which is regarded as being imbedded in a statistical structure emulates the characteristic of rest mass. The average energy and momentum of this statistical system are then shown to satisfy the usual classical relativistic relation between energy and momentum. The statistical structure chosen is that of an object with a randomly orientated velocity vector, c, which has a fixed magnitude c … |c| where c is the velocity of light.
Interaction between migration and breeding studied by means of genetic algebras
Authors: Holgate P.
Published: April 2006

In this paper the theory of genetic algebras introduced by Etherington [3], [5] is developed to cover the case where the population is divided into a number of partially isolated subpopulations, between which a limited amount of migration is permitted. It is known [3], [6], [7], [8], [10], that in the absence of selective factors most genetic segregation systems can be represented by algebras belonging to the class of special train algebras, discussed in detail in [4].
Carrier-borne epidemics with immigration. I — Immigration of both susceptibles and carriers
Authors: Dietz K. , Downton F.
Published: April 2006

Much of the theory of epidemics (see Bailey, 1957) has been concerned with models for their behaviour in closed populations. In such models the epidemic ultimately dies out, and interest has been concentrated on, for example, the ultimate size of the epidemic and its duration in time. In practice a population is rarely completely closed, and for many diseases an endemic model rather than an epidemic model is appropriate. To create models for endemic diseases it is necessary to introduce both new persons susceptible to the disease into the population and new sources of infection. For the so-called general stochastic epidemic, Ridler-Rowe (1967) has obtained certain limiting properties of the population where immigration of both susceptibles and infectives into the population takes place, but much work remains to be done to obtain, for example, the general equilibrium behaviour of this model.
Programming problems and changes in the stable behavior of a class of Markov chains
Authors: Evans Richard V.
Published: April 2006

This paper develops expressions for the derivatives with respect to a parameter μ of the stable probabilities of a class of Markov chains whose transition matrices are of the form Q + μW. These expressions lead to iterative schemes for calculation which in turn suggest gradient algorithms for finding locally optimal chains.
Poisson recurrence times
Authors: Dwass Meyer
Published: April 2006

Let Y1, Y2, … be a sequence of independent and identically distributed Poisson random variables with parameter λ. Let Sn = Y1 + … + Yn, n = 1,2,…, S0 = 0. The event Sn = n is a recurrent event in the sense that successive waiting times between recurrences form a sequence of independent and identically distributed random variables. Specifically, the waiting time probabilities are

(Alternately, the fn can be described as the probabilities for first return to the origin of the random walk whose successive steps are Y1 − 1, Y2 − 1, ….)
On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times
Authors: Loris-Teghem Jacqueline
Published: April 2006

A generalized queueing system with (N + 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform.

The standard Kl/Km/1 queueing system with uniformly bounded sojourn times is considered in particular.
On an epidemic in a stratified population
Authors: Watson R. K.
Published: April 2006

Most epidemic models previously studied have assumed a homogeneously mixing population. Instead of making this assumption, a population divided into classes is considered; and it is assumed that the degree of mixing between classes is less than that within classes. The stochastic model in this form is intractable and approximations are made, yielding results in reasonable agreement with simulation trials.
An extension of a theorem concerning an interesting Markov chain
Authors: Hendricks W. J.
Published: April 2006

In a single-shelf library of N books we suppose that books are selected one at a time and returned to the kth position on the shelf before another selection is made. Books are moved to the right or left as necessary to vacate position k. The probability of selecting each book is assumed to be known, and the N! arrangements of the books are considered as states of an ergodic Markov chain for which we find the stationary distribution.
A note on the central limit theorem for doubly stochastic Poisson processes
Authors: Rootzén Holger
Published: April 2006

In this note, necessary and sufficient conditions for the central limit theorem for the number of events in a doubly stochastic Poisson process are given.
A note on the recurrence of yellow fever epidemics in urban populations
Authors: Radcliffe J.
Published: April 2006

An approximate expression is found for the probability density of the recurrence time between major outbreaks of a host-vector disease such as yellow fever, in which the infectious period of a host is short and the lifetime of a vector is short compared with that of a host. The typical interval between epidemics based on the modal value of this distribution is obtained. These results are the analogues of those obtained by Bartlett (1956), (1966) for the periodicity of measles epidemics in small communities.
A comparison of linear versus non-linear prediction for polynomial functions of the Ornstein-Uhlenbeck process
Authors: III John Donelson , Maltz Fred
Published: April 2006

The general minimum mean square error prediction problem is studied for the class of processes defined by polynomial functions of the Ornstein-Uhlenbeck process. In particular, the relative error difference for non-linear prediction compared with optimal linear prediction is calculated. Limiting values are determined, including an upper bound for the maximal relative error difference. These results show no difference over the entire class for both long and short prediction lead times. For a single Hermite polynomial, the relative error difference is zero. An analytical solution for the maximal difference for lead times below a given threshold is derived. This latter result has been verified numerically on a digital computer for polynomials up to 17th degree.
Maximum likelihood estimation for stochastic rth -order reactions
Authors: Mullooly John P.
Published: April 2006

In this paper we derive the probability distributions of the number of molecules and of the lifetime of a molecule in a stochastic rth-order system by direct evaluation of probabilities, avoiding the use of differential-difference equations. Maximum likelihood estimation of the rate constant is based on an observation of the level of the system at time t > 0. We find the asymptotic solution of the likelihood equation for a large initial number of molecules. By comparison with the numerical solution of the likelihood equation, the asymptotic estimator is shown to be a satisfactory approximation for second order reactions which are far from completion.
On the relationship between the distribution of maximal queue length in the M/G/1 queue and the mean busy period in the M/G/1/n queue
Authors: Cooper Robert B. , Tilt Borge
Published: April 2006

Takács has shown that, in the M/G/1 queue, the probability P(k | i) that the maximum number of customers present simultaneously during a busy period that begins with i customers present is P(k | i) = Qk–i/Qk, where the Q's are easily calculated by recurrence in terms of an arbitrary Q0 ≠ 0. We augment Takács's theorem by showing that P(k | i) = bk–i/bk, where bn is the mean busy period in the M/G/1 queue with finite waiting room of size n; that is, if we take Q0 equal to the mean service time, then Qn =bn.
Some approximate results for storage systems with continuous inputs
Authors: Herbert H. G.
Published: April 2006

Some approximate results for infinite capacity storage systems in which the input rate follows a birth and death process are given in this paper. In particular, an immigration-emigration process and an Ehrenfest process are considered. The almost-null-recurrent content distribution is derived when the demand rate is constant. Further, an approximation for the content distribution during a period of excessive over-supply is obtained for the cases of constant demand and demand proportional to the content.
Some inequalities on variances
Authors: Goldstein Matthew
Published: April 2006

Sharp upper and lower bounds for the variance of a non-negative function of a non-negative random variable are obtained under rather weak hypotheses regarding the function. Comparisons between bounds are made and some specific examples are considered.
An infinite discrete dam with dependent inputs
Authors: Herbert H. G.
Published: April 2006

This paper is concerned with an infinite discrete dam fed by inputs which form a moving average sequence. Generating functions are derived for the joint time dependent distribution of the content, accumulated input and total dry time, the distribution of first emptiness, and the stationary content distribution. Also investigated is the problem of first emptiness before overflow for the finite dam.
Limit distributions of the number of renewals and waiting times
Authors: Mohan N. R.
Published: April 2006

Let {Xn} be an infinite sequence of independent non-negative random variables. Let the distribution function of Xi, i = 1, 2, …, be either F1 or F2 where F1 and F2 are distinct. Set Sn = X1 + X2 + … + Xn and for t > 0 define and Zt = SN(t)+1 – t. The limit distributions of N(t), Yt and Zt as t → ∞ are obtained when F1 and F2 are in the domains of attraction of stable laws with exponents α1 and α2, respectively and Sn properly normalised has the composition of these two stable laws as its limit distribution.
On the equivalence of certain Markov chains
Authors: Vit Pedro
Published: April 2006

It is shown that an irreducible and aperiodic Markov chain can be altered preserving irreducibility without altering the nature of the chain in the sense that, the modified chain is transient (recurrent) if and only if the original chain is transient (recurrent). Furthermore, it is shown by means of a counterexample that ergodicity (null-recurrence) is not preserved.

An interesting application of this result is a simple proof of Pakes's generalization of Foster's criterion for a chain to be recurrent.
Two characterizations of the geometric distribution
Authors: Arnold Barry C.
Published: April 2006

Let X1, X2, …, Xn be independent identically distributed positive integer-valued random variables with order statistics X1:n, X2:n, …, Xn:n. If the Xi's have a geometric distribution then the conditional distribution of Xk+1:n – Xk:n given Xk+1:n – Xk:n > 0 is the same as the distribution of X1:n–k. Also the random variable X2:n – X1:n is independent of the event [X1:n = 1]. Under mild conditions each of these two properties characterizes the geometric distribution.
Multiserver scheduling of jobs with increasing completion rates
Authors: Gittins J. C.
Published: April 2006

Under certain conditions it is shown that for jobs with increasing completion rates the expected flow time is minimised by a non-pre-emptive service discipline.
A local limit theorem for the critical age-dependent branching process
Authors: Quigg David L.
Published: April 2006

Let Z(t) denote the number of particles alive at time t in a critical age-dependent branching process. It is proved that, for k ≧ 1, there exists a constant Ak > 0 such that t2P(Z(t) = k)→Ak as t→∞.
The expected number of visits of a sequence of normal partial sums to each side of a boundary
Authors: Pollar Moshe
Published: April 2006

Let be the sequence of partial sums of independent N(μ, 1) random variables. The boundary in the {(n, Sn)} plane which minimizes the expected number of times n that Sn will be below a boundary when μ = θ > 0 subject to a given expected number of visits that Sn will be above the same boundary when μ = 0 is shown to be linear and is also characterized. Similar results are shown for Brownian motion.
An analysis of the fixed-cycle traffic-light problem
Authors: Cowan Richard
Published: April 2006

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.
Random space filling and moments of coverage in geometrical probability
Authors: Siegel Andrew F.
Published: April 2006

The moments of the random proportion of a fixed set that is covered by a random set (moments of coverage) are shown to converge under very general conditions to the probability that the fixed set is almost everywhere covered by the random set. Moments and coverage probabilities are calculated for several cases of random arcs of random sizes on the circle. When comparing arc length distributions having the same expectation, it is conjectured that if one concentrates more mass near that expectation, the corresponding coverage probability will be smaller. Support for this conjecture is provided in special cases.
The second moments of the absorption times in the Markov renewal branching process
Authors: Neuts Marcel F.
Published: April 2006

We derive explicit formulas for the second moments of the absorption time matrices in the Markov renewal branching process. These formulas may easily be computationally implemented and are useful in the iterative computation of the semi-Markov matrices, which give the distributions of the duration and of the number of customers served in a busy period of a great variety of complex queueing models.
The limit distribution for maxima of ‘weighted' rth-nearest-neighbour distances
Authors: Henze Norbert
Published: April 2006

Let X1, X2, · ··, Xn be independent identically distributed random points with common density f(x), taking values in a bounded region (p ≧ 1). We obtain the limit distribution, as n → ∞, for the maximum value of the suitably ‘weighted' (according to f(x)) rth-nearest-neighbour distances of Χ1, · ··, Χ n (r ≧ 1 fixed) provided that f(x) is bounded from below by a positive constant and a weak continuity condition holds. This is achieved by refining an argument used by the author (Henze (1981)) to derive the limit distribution in the special case r = 1. Edge-effects are eliminated by defining, for each Xi, the distance to the boundary of G to be the ‘rth-nearest-neighbour distance' if it is smaller than the distance to the rth nearest neighbour among the remaining points. Applications to a multivariate test of goodness of fit are given.
Some comparability results for waiting times in single- and many-server queues
Authors: Daley D. J. , Rolski T.
Published: April 2006

It is shown that the stationary waiting time random variables W′, W″ of two M/G/l queueing systems for which the corresponding service time random variables satisfy E(S′−x)+ ≦ E(S″−x)+ (all x >0), are stochastically ordered as W′≦dW″. The weaker conclusion, that E(W′−x)+ ≦ E(W″−x)+ (all x > 0), is shown to hold in GI/M/k systems when the interarrival time random variables satisfy E(x−T′)+ ≦ E(x−T″)+ (all x). A sufficient condition for wk≡EW in GI/D/k to be monotonic in k for a sequence of k-server queues with the same relative traffic intensity is given. Evidence indicating or refuting possible strengthenings of some of the results is indicated.
Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes
Authors: Eplett W. J. R.
Published: April 2006

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.
Filtering counts of cars entering and leaving a parking place
Authors: Andersen Søren , Rudemo Mats
Published: April 2006

Cars entering and leaving a parking place in a forest are registered automatically in connection with an investigation of forest recreational use. By subtraction the number of cars parked is computed. Due to erroneous and missing counts, errors occur and may for instance indicate a negative number. The theory of incompletely observed Markov chains is used to obtain an estimate of the number of cars parked.
Asymptotic properties of stereological estimators of volume fraction for stationary random sets
Authors: Mase Shigeru
Published: April 2006

We shall discuss asymptotic properties of stereological estimators of volume (area) fraction for stationary random sets (in the sense of Matheron) under natural and general assumptions. Results obtained are strong consistency, asymptotic normality, and asymptotic unbiasedness and consistency of asymptotic variance estimators. The method is analogous to the non-parametric estimation of spectral density functions of stationary time series using window functions. Proofs are given for areal estimators, but they are also valid for lineal and point estimators with slight modifications. Finally we show that stationary Boolean models satisfy the relevant assumptions reasonably well.
On a theorem of bingham and doney
Authors: De Meyer A.
Published: April 2006

We obtain an extension of a theorem of Bingham and Doney connecting the random variables Z1 and W in the supercritical Galton-Watson process. The regular variation of the distribution of Z1 is equivalent to the regular variation of the tail of the distribution of W for integer values of α > 1.
Bellman–Harris branching processes with state-dependent immigration
Authors: Mitov K. V. , Yanev N. M.
Published: April 2006

We consider critical Bellman-Harris processes which admit an immigration component only in the state 0. The asymptotic behaviour of the probability of extinction and of the first two moments is investigated and a limit theorem is also proved.
Optimal search for a randomly moving object
Authors: Weber R. R.
Published: April 2006

It is desired to minimize the expected cost of finding an object which moves back and forth between two locations according to an unobservable Markov process. When the object is in location i (i = 1, 2) it resides there for a time which is exponentially distributed with parameter λ1 and then moves to the other location. The location of the object is not known and at each instant until it is found exactly one of the two locations must be searched. Searching location i for time δ costs ciδ and conditional on the object being in location i there is a probability αiδ + o(δ) that this search will find it. The probability that the object starts in location 1 is known to bé p1(0). The location to be searched at time t is to be chosen on the basis of the value of p1(t), the probability that the object is in location 1, given that it has not yet been discovered. We prove that there exists a threshold Π such that the optimal policy may be described as: search location 1 if and only if the probability that the object is in location 1 is greater than Π. Expressions for the threshold Π are given in terms of the parameters of the model.
Exponential martingales and Wald's formulas for two-queue networks
Authors: Baccelli François
Published: April 2006

An exponential martingale is defined for a class of random walks in the positive quarter lattice which are associated with a wide variety of Markovian two-queue networks. Balance formulas generalizing Wald's exponential identity are derived from the regularity of several types of hitting times with respect to this martingale. In a queuing context, these formulas can be interpreted as functional relations of practical interest between the number of customers at certain epochs and the utilization of the queues up to these epochs.
Simulated annealing methods with general acceptance probabilities
Authors: Anily S. , Federgruen A.
Published: April 2006

Heuristic solution methods for combinatorial optimization problems are often based on local neighborhood searches. These tend to get trapped in a local optimum and the final result is often heavily dependent on the starting solution. Simulated annealing methods attempt to avoid these problems by randomizing the procedure so as to allow for occasional changes that worsen the solution. In this paper we provide probabilistic analyses of different designs of these methods.
Optimal stopping in a continuous search model
Authors: Zuckerman Dror
Published: April 2006

We examine a continuous search model in which rewards (e.g. job offers in a search model in the labor market, price offers for a given asset, etc.) are received randomly according to a renewal process determined by a known distribution function. The rewards are non-negative independent and have a common distribution with finite mean. Over the search period there is a constant cost per unit time. The searcher's objective is to choose a stopping time at which he receives the highest available reward (offer), so as to maximize the net expected discounted return. If the interarrival time distribution in the renewal process is new better than used (NBU), it is shown that the optimal stopping strategy possesses the control limit property. The term ‘control limit policy' refers to a strategy in which we accept the first reward (offer) which exceeds a critical control level ξ.
Transient analysis of M/M/1 queues in discrete time by general server vacations
Authors: Böhm W. , Mohanty S. G.
Published: April 2006

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.
On termination time processes
Authors: Dshalalow Jewgeni H.
Published: April 2006

In this paper we study the behavior of a delayed compound renewal process, S, about some fixed level, L. Normally, a jump process S increases at random times τ1, τ2, …, in random increments until it crosses L. S would then be terminated in a random number v of phases at time τv. In many applications, a more general termination scenario assumes that S may evolve either through v or σ random phases, whichever of the two is smaller (denoted by T). The number T of actual phases is called the termination index, and we evaluate a joint functional of T, the termination time τ T and the termination level ST. We also seek information about the process S a step before its termination, and derive a joint functional for all relevant processes. Examples of these processes and their applications to various stochastic models are discussed.
Stochastic models of damped vibrations
Authors: Elshamy Maged
Published: April 2006

In this article we study stochastic perturbations of partial differential equations describing forced-damped vibrations of a string. Two models of such stochastic disturbances are considered; one is triggered by an initial white noise, and the other is in the form of non-Gaussian random forcing. Let uε (t, x) be the displacement at time t of a point x on a string, where the time variable t ≧ 0, and the space variable . The small parameter ε controls the intensity of the random fluctuations. The random fields uε (t, x) are shown to satisfy a large deviations principle, and the random deviations of the unperturbed displacement function are analyzed as the noise parameter ε tends to zero.
From FIFO to LIFO: a functional ordering of service delay via arrival discipline
Authors: Li Jingwen
Published: April 2006

Vasicek (1977) proved that among all queueing disciplines that do not change the departure process of the queue, FIFO and LIFO yield, respectively, the smallest and the largest expectation of any given convex function of the service delay. In this note we further show that, if arriving customers join the queue stochastically ‘closer' to the server(s), then the expected value of any convex function of service delay is larger. As a more interesting result, we also show that if the function under consideration is concave, then the conclusion will be exactly the opposite. This result indicates that LIFO will be the best discipline if the delay cost is an increasing function but at a diminishing rate.