bluuebunny/crossref_metadata_2025 huggingface dataset:
General Committee Report 4
Authors: Nicolson Dan H.
Published: April 2006

Nicolson, D. H.: General Committee Report 4. ‐ Taxon 42: 110‐111. 1993. ‐ ISSN 0040‐0262.

The General Committee approves proposals recommended by Bryophyta Committee Report 1 (9) and Spermatophyta Committee Report 37 (12, including a confusability decision). One decision not to recommend is returned to the Spermatophyta Committee for reconsideration under new instructions.
ON DIMENSIONS OF TYPICAL FORMS OF COLEOCHAETE (CHAROPHYCEAE) SPECIES DESCRIBED BY PRINGSHEIM
Authors: Szymańska Hanna
Published: April 2006

The dimensions of typical forms of six species of Coleochaete: C. scutata, C. pulvinata, C. soluta, C. divergens, C. irregularis, and C. orbicularis, have been continuously overestimated due to a misinterpretation of an original account by Pringsheim (1860). In this paper correct dimensions are given, and ‘small’ forms of the species are discussed, most of them being found superfluous.
Report of the Committee for Fungi: 5
Authors: Gams Walter
Published: April 2006

Gams, W.: Report of the Committee for Fungi: 5. – Taxon 44: 411‐414. 1995. – ISSN 0040‐0262.

The Committee for Fungi reports action on 19 proposals to conserve or reject names, recommending 14.
The typification of Piptolepis Sch. Bip. (Compositae), nom cons.
Authors: Jeffrey C. , Hind D. J. N.
Published: April 2006

Jeffrey, C. J. & Hind, D. J. N.: The typification of Piptolepis Sch. Bip. (Compositae), nom cons. – Taxon 43: 94‐96. 1994. – ISSN 0040‐0262.

To maintain stability of the generic name for this characteristic Brazilian taxon, the original and correct type citation should be used. It is recommended that the type citation in Appendix IIIA of the Code be corrected to: “Piptolepis ericoides Sch. Bip., Jahresber. Pollichia 20/21: 383. 1863”, lectotypified here.
A reappraisal of the generic status of Liparia and Priestleya (Fabaceae)
Authors: Schutte Anne Lise , Van Wyk Ben‐Erik
Published: April 2006

Schutte, A. L. & Van Wyk, B‐E.: A reappraisal of the generic status of Liparia and Priestleya (Fabaceae). – Taxon 43: 573‐582. 1994. – ISSN 0040‐0262.

The generic delimitation of Liparia L. and Priestleya DC. (Fabaceae, tribe Liparieae) is reevaluated. Traditionally the shape and size of the carinal lobe of the calyx, the shape of the keel petals and the number of flowers per inflorescence were used as diagnostic characters. A study of morphological and alkaloid variation indicates that the two genera run much into one another. Differences in inflorescence and floral structure can be attributed to adaptations to different pollination strategies. The unique combination of major alkaloids occurring in both genera also suggests that they are congeneric. Priestleya is therefore placed into synonymy under Liparia. The nomenclature, synonymy and typification of the genus and the 14 species recognized are presented, and some necessary new combinations are made.
Taxonomic and nomenclatural notes on Anotrichium tenue and related species (Ceramiaceae, Rhodophyta)
Authors: Cormaci Mario , Furnari Giovanni , Pizzuto Fabio
Published: April 2006

Cormaci, M., Furnari, G. & Pizzuto, F.: Taxonomic and nomenclatural notes on Anotrichium tenue and related species (Ceramiaceae, Rhodophyta). – Taxon 43: 633‐637. 1994. – ISSN 0040‐0262.

Two distinct species, differing mainly in tetrasporangial features, have been confused under the name Anotrichium tenue. In true A. tenue the tetrasporangia are borne terminally on a small number (5‐8) of whorled pedicels. In the other, A. secundum, comb, nov., the tetrasporangia are borne subterminally and adaxially on a relatively large number (8‐50) of whorled pedicels.
Typification and the names of fossil plants – a review and discussion
Authors: Fensome Robert A. , Jansonius Jan , Skog Judith E.
Published: April 2006

Fensome, R. A., Jansonius, J. & Skog, J. E.: Typification and names of fossil plants – a review and discussion. – Taxon 47: 695‐702. – ISSN 0040‐0262.

The rules surrounding the designation of nomenclatural types to fossil plant taxa, including the definitions of the various kinds of type and the related requirements for valid publication, are found in several provisions of the International code of botanical nomenclature. In part because of the necessarily piecemeal nature of these rules, problems and ambiguities in interpretation have arisen that merit discussion. These problems and ambiguities include: the definition of the term lectotype; the use of isotypes and epitypes; the appropriate treatment of macrofossil types that are represented by more than one specimen; the application of Article 37.4 and the citation of collectors' names; the nature of the type of a generic name; the definition of “original material”; and the imperative to indicate the repository of a type. In our view, the increasing rate of change of the Code, which would reach a climax with the possible introduction of a BioCode, is also promoting ambiguities, and hence potential instability in plant nomenclature.
Lectotypification of 16 species names in Doronicum (Asteraceae, Senecioneae)
Authors: Fernández Inés Álvarez , Feliner Gonzalo Nieto
Published: April 2006

Álvarez Fernández, I. & Nieto Feliner, G.: Lectotypification of 16 species names in Doronicum (Asteraceae, Senecioneae). ‐‐ Taxon 48: 801‐806. 1999. – ISSN 0040‐0262.

16 binomials in Doronicum are lectotypified. All are either accepted names of species or basionyms of accepted subspecies names, in a forthcoming taxonomic revision of the genus.
Paleobotany: some aspects of non‐flowering and flowering plant evolution
Authors: Dilcher David L.
Published: April 2006

Dilcher, D. L.: Paleobotany: some aspects of non‐flowering and flowering plant evolution. ‐Taxon 50: 697–711. 2001. ‐ ISSN 0040‐0262.

When an examination of some aspects of the evolution of vascular land plants is made across broad sweeps of Paleozoic, Mesozoic and Tertiary time, three basic patterns occur in unrelated groups in vascular land plant evolution: independent evolution of similar morphologies, nearly contemporaneous evolution of similar structures and strategies, and repeated evolution of similar features or strategies at different times. Examples are given in non‐flowering plants and also in the evolution of angiosperms. A database is presented to illustrate the presence of angiosperms in the Jurassic/Lower Cretaceous fossil record and the diversity and abundance of organs recovered from these early angiosperms. These data are presented as working documents with the anticipation that they may grow into a major database for interested scholars world‐wide.
The contribution of micromorphology to the taxonomy and fossil record of the Myricaceae
Authors: Ferguson David K.
Published: April 2006

Ferguson, D. K.: The contribution of micromorphology to the taxonomy and fossil record of the Myricaceae. – Taxon 47: 333‐335.1998. – ISSN 0040‐0262.

Micromorphological characters assist in the circumscription of the family Myricaceae and can be used to distinguish the segregate genera. The fossil record is based on leaf compressions, fruits and pollen grains. In the Tertiary the commonest genus was Myrica sensu stricto.
Intermediacy between Grindelia chiloensis and Haplopappus pectinatus (Astereae, Asteraceae)
Authors: Bartoli Adriana , Tortosa Roberto D.
Published: April 2006

Bartoli, A. & Tortosa, R. D.: Intermediacy between Grindelia chiloensis and Haplopappus pectinatus (Astereae, Asteraceae). – Taxon 47: 337‐345. 1998. – ISSN 0040‐0262.

Intermediate specimens between Grindelia chiloensis and Haplopappus pectinatus occur in Patagonia (Argentina). They were analysed using the methods proposed by Wells (distance diagram) and Wilson (character count procedure). With both methods the hypothesis of hybridity is supported. A close proximity of H. pectinatus to the genus Grindelia is also suggested by a high percentage of stainable pollen grains in the putative hybrids, chromosome morphology, and achene anatomy. Based on such evidence, the new combination G. anethifolia (H. pectinatus Phil., non G. pedinata Baker) is proposed.
Achyrothalamus reduced to Erythrocephalum (Asteraceae, Mutisieae)
Authors: Ortiz Santiago , Coutinho Antonio P.
Published: April 2006

Ortiz, S. & Coutinho, A. P.: Achyrothalamus reduced to Erythrocephalum (Asteraceae, Mutisieae). – Taxon 50: 389–403. 2001. – ISSN 0040‐0262.

The monotypic genus Achyrothalamus has been conventionally distinguished from Erythrocephalum principally by the absence of a pappus and the presence of phyllaries with entire margins. However, a critical re‐examination of 83 morphological and anatomical characters, and a detailed study of the pollen of the two genera, suggest that recognition of Achyrothalamus as a distinct genus is unjustified. We thus propose Achyrothalamus as a synonym of Erythrocephalum with the new combination E. marginatum.
Distribution and diagnostic characters of Nassella (Poaceae: Stipeae)
Authors: Barkworth Mary E. , Torres María Amelia
Published: April 2006

Barkworth, M. E. & Torres, M. A.: Distribution and diagnostic characters of Nassella (Poaceae: Stipeae). – Taxon 50: 439–468. 2001. – ISSN 0040‐0262.

Nassella sensu lato includes 116 species, making it one of the largest genera in tribe Stipeae. Argentina has the largest number of species, 72, with the greatest concentration being in the northwestern part of the country. Bolivia, Chile, and Uruguay have 26, 27, and 27 species, respectively. Other South American countries in which the genus is present are Brazil (18 species), Colombia (8), Ecuador (9), Paraguay (4), Peru (18), and Venezuela (2). Guatemala has two species, but Costa Rica only one. Mexico has eight native species, five of which also grow in the United States. One additional species grows in both the United States and Canada. Sixty species are known only from one country; one species, N. mexicana, grows in eight countries. Several new distribution records are documented: N. caespitosa, N. elata, N. leptothera and N. punensis for Bolivia, N. pauciciliata and N. spegazzinii for Brazil, N. airoides, N. argentinensis, N. spegazzinii for Paraguay, and N. tucumana (= N. asperifolia) for Peru. Three new combinations are presented: N. burkartii, N. ligularis, and N. quinqueciliata. Two recently transferred species, N. barrancaensis and N. brachychaeta, are excluded from the genus and N. asperifolia, N. bonariensis, and N. amethystina are placed in synonymy. Tables summarising the distribution of Nassella and its morphological variation are presented.
Naming the groups: developing a stable and efficient nomenclature
Authors: McNeill John
Published: April 2006

McNeill, J.: Naming the groups: developing a stable and efficient nomenclature. – Taxon 49: 705–720. – ISSN 0040‐0262.

The binomial system of botanical nomenclature has existed for almost 250 years, the principle of a taxon having a single correct name determined on the basis of priority of publication was formalized almost 150 years ago, and the type method for the application of scientific names of plants has had international acceptance for almost 75 years. In this historic time‐frame, the achievements of the past 50 years are outlined and the question posed as to whether the next 50 years hold any prospect of change, and indeed whether any change is possible or even desirable. The requirement of botanical nomenclature to provide a stable, unambiguous reference system for plant information implies an inherent conservatism of rules and procedures—even the smallest change to the Code, however beneficial it may be in general, is virtually certain to have some destabilizing effect. Despite this truism, it is suggested that the next few years will see quite major change. One of the least of these may be the development of a separate specialist nomenclature for communication about major phyletic lineages, not so dissimilar in practice from the specialist nomenclature currently in existence for the micro‐variants important in cultivated plants. Bionomenclature provides the mechanism for communication about the elements of taxonomy—elements that generally seek to reflect the greatest information on patterns of biodiversity. It will continue to communicate the general information content of taxa effectively, only if it evolves to take fuller advantage of the opportunities of the electronic age. The historical tendency to improve the rules of nomenclature by continuous “tinkering” with the Code needs to give way to a recognition that stability and simplicity are key requirements of users of names (amongst whom professional biologists are a relatively small minority), and that web access to authoritative lists will generally be their preferred approach to answering the nomenclatural questions that arise in study and use of plants, animals and micro‐organisms. To remain relevant, the botanical Code, like the bacteriological, and now, to a degree, the zoological, must provide mechanisms for the endorsement of nomenclatural lists that represent the products of sound scholarship.
The identity of Dicoma bangueolensis (Asteraceae)
Authors: Ortiz Santiago , Rodríguez‐Oubiña Juan
Published: April 2006

Ortiz, S. & Rodríguez‐Oubiña, J.: The identity of Dicoma bangueolensis (Asteraceae). – Taxon 45: 519‐520. 1996. – ISSN 0040‐0262.

Dicoma bangueolensis, lectotypified here, is a common species of Somalia, not of Tanzania as fraudulently claimed by Muschler in the protologue.
Reappraisal of Cololejeunea ceratilobula, C. formosana, and C. reineckeana (Hepaticae, Lejeuneaceae)
Authors: Rui‐Liang Zhu , Ling So May
Published: April 2006

Zhu, R.‐L. & So, M. L.: Reappraisal of Cololejeunea ceratilobula, C. formosana, and C. reineckeana (Hepaticae, Lejeuneaceae). – Taxon 47: 839‐842. 1998. – ISSN 0040‐0262.

Cololejeunea formosana Mizut., whose correct name is C. ceratilobula (P. C. Chen) R. M. Schust., was earlier considered as synonymous with C. reineckeana Steph. but belongs to C. subg. Chlorocolea, whereas C. reineckeana is a member of C. subg. Pedinolejeunea. A description and illustration of C. reineckeana are provided.
Transfers from Amaryllis to Hippeastrum (Amaryllidaceae)
Authors: Meerow Alan W. , Van Scheepen Johan , Dutilh Julie H. A.
Published: April 2006

Meerow, A. W., Van Scheepen, J. & Dutilh, J. H. A.: Transfers from Amaryllis to Hippeastrum (Amaryllidaceae). – Taxon 46: 15‐19. 1997. – ISSN 0040‐0262.

42 species transfers are made from Amaryllis to Hippeastrum in accord with the decision, at the Fourteenth International Botanical Congress in 1987, on the application of the former name to a South African genus. This completes the validation of combinations required in Hippeastrum, and will thus aid nomenclatural clarity and enable botanists and horticulturists to refer to these species by their correct names.
A method to establish and revise descriptive data sets over the Internet
Authors: Hagedorn Gregor , Rambold Gerhard
Published: April 2006

Hagedorn, G. & Rambold, G.: A method to establish and revise descriptive data sets over the internet. ‐ Taxon 49: 517–528. 2000. ‐ ISSN 0040‐0262.

In science, the internet is used at present mostly as an electronic publishing tool. It is highly desirable to increasingly use it as a working and production tool for collaborative projects in taxonomy and biodiversity as well. The method described here requires neither programming nor web‐server expertise. Provided that the DELTA data standard is used, projects can be imported into the DeltaAccess database application. Using HTML data submission forms automatically generated from the database, projects can then be established and interactively revised over the internet. The forms permit adding new information as well as revising existing information. They are user‐platform independent and require only standard web browser functionality. This standard‐based approach avoids the repeated development of tools for using the internet as a working space. The DeltaAccess application is distributed over the internet under a General Public License.
A new online bibliographic database of proposals for conservation and rejection of botanical names
Authors: Nicolson Dan H.
Published: April 2006

Nicolson, D. H.: A new online bibliographic database of proposals for conservation and rejection of botanical names. ‐ Taxon 49: 549–554. 2000. ‐ ISSN 0040‐0262.

As of mid‐2000 over 4,400 proposals have been made to conserve and/or reject botanical names, almost all at the rank of family, genus or species. Information on all proposals has been compiled, including the author and places of publication of each proposal, as well as the place of publication of the report on the proposals by the Committees for particular groups, the General Committee report, where cited in a Synopsis of Proposals, where ratified by a Congress, and where each of the approved proposals first appeared in a Code. With nearly 3000 of these names already in the Code the success rate of proposals approaches two‐thirds. This compiled information is accessible and searchable online: .
Extending Gower's general coefficient of similarity to ordinal characters
Authors: Podani János
Published: April 2006

Podani, J.: Extending Gower's general coefficient of similarity to ordinal characters. – Taxon 48: 331‐340. 1999. – ISSN 0040‐0262.

The possibilities of calculating similarity based on ordinal characters are evaluated by distinguishing subtypes of the ordinal scale. Multivariate analysis is most problematic when ordinal variables appear together with other scale types in the data. This difficulty is solved by extending Gower's general coefficient of similarity to ordinal data types, facilitating cluster analysis and multidimensional scaling. Two alternatives, a non‐metric and a metric version, are offered. The modified formula implies that ordinal variables are equally weighted with the others, and that partially and fully ranked data are both applicable, due to the inherent standardisation procedure. A morphological data set derived for the moss genus Tortula illustrates the new approach.
Validation of Qiongzhuea and correlated species names (Gramineae, Bambusoideae)
Authors: Hsueh C. J. , Yi Tong‐pei , Li De‐zhu
Published: April 2006

Hsueh, C. J., Yi, T. P. & Li, D. Z.: Validation of Qiongzhuea and correlated species names (Gramineae, Bambusoideae). – Taxon 45: 217‐221. 1996. – ISSN 0040‐0262.

Qiongzhuea, when first published, was based on “Q. tumidinoda” as designated type. However, the latter name was not validly published because two different type specimens were cited, therefore the generic name, and all specific names that were subsequently published under it, are not valildly published either. A new name for Q. tumidinoda was later validated by Ohrnberger under Chimonobambusa, C. tumidissinoda, whereas the generic name still needs to be validated. The terms and conditions are here met for validating the name Qiongzhuea, and all species names concerned, under the provisions of the Code.
The stochastic equation Yn+1=AnYn + Bn with stationary coefficients
Authors: Brandt Andreas
Published: April 2006

In this note we deal with the stochastic difference equation of the form Yn+1 = AnYn + Bn, n∊ℤ, where the sequence is assumed to be strictly stationary and ergodic. By means of simple arguments a unique stationary solution of this equation is constructed. The stability of the stationary solution is the second subject of investigation. It is shown that under some additional assumptions
PhyloCode ­ pain, no gain
Authors: Forey Peter L.
Published: April 2006

The PhyloCode suggests that by adopting its rules, taxonomists will gain clarity, uniqueness and stability compared with the use of Linnaean Taxonomy. This claim is questioned here by suggesting (1) that replacing the Types of Linnaean Taxonomy with the Specifiers of PhyloCode increases the complexity of decisions which have to be made, some of which go beyond nomenclature; (2) deciding which PhyloCode definition of a name to use demands knowledge of phylogenetic support and likelihood of future changes in ideas of relationships; (3) Phylogenetic Nomenclature will have limited value because it names only monophyletic groups, and (4) confusion over naming taxa is not avoided by the PhyloCode and can lead to problems when used alongside Linnaean Taxonomy. The problems concerning Linnaean rank and raised by Phylogenetic Nomenclature are upheld.
Green algae (Chlorophyta) of desert microbiotic crusts: diversity of North American taxa
Authors: Lewis Louise A. , Flechtner Valerie R.
Published: April 2006

Green algae are present in desert soils as components of microbiotic communities that also include cyanobacteria and other prokaryotes, lichens, non­lichenized fungi, invertebrates, and other photosynthetic eukaryotes such as diatoms, eustigmatophytes, and xanthophytes. The green algae that occur in crusts are morphologically simple unicells, packets of cells, or weak filaments, yet represent a diverse assemblage of taxa spanning the classes Chlorophyceae, Trebouxiophyceae, and Charophyceae. As part of an ongoing study of the biodiversity of microbiotic crust communities in the western United States and Northern Mexico, a large number of green algae were isolated and characterized morphologically and genetically. Phylogenetic analyses using ribosomal RNA gene sequence data have greatly aided our understanding of the diversity and evolution of desert green algae. Our results indicate that desert green algae evolved from aquatic green algae at least five independent times. In addition, the desert green algae are derived from freshwater, not marine, green ancestors. Some lineages of green algae have a high proportion of desert taxa, while other lineages thus far have no known desert representatives. Many of the isolates are likely to be new taxa. These taxa represent independent lineages of green plants that have evolved to inhabit desert environments. Because they are distinct from but phylogenetically related to embryophyte taxa, these other "land plants" can offer important biochemical and physiological comparisons to desert­dwelling embryophytes.
Does Compulsory School Attendance Affect Schooling and Earnings?
Authors: Angrist Joshua D. , Krueger Alan B.
Published: April 2006

We establish that season of birth is related to educational attainment because of school start age policy and compulsory school attendance laws. Individuals born in the beginning of the year start school at an older age, and can therefore drop out after completing less schooling than individuals born near the end of the year. Roughly 25 percent of potential dropouts remain in school because of compulsory schooling laws. We estimate the impact of compulsory schooling on earnings by using quarter of birth as an instrument for education. The instrumental variables estimate of the return to education is close to the ordinary least squares estimate, suggesting that there is little bias in conventional estimates.
Truncation procedures for non-negative matrices
Authors: Tweedie Richard L.
Published: April 2006

1. Let T = (tij), i, j = 0, 1, ···, tij ≧ 0, denote an infinite non-negative matrix. We shall assume at all times that where are the matrix iterates of T; we take T0 = I = (δij).
Occupation times for two state Markov chains
Authors: Pedler P. J.
Published: April 2006

Consider first a Markov chain with two ergodic states E1 and E2, and discrete time parameter set {0, 1, 2, ···, n}. Define the random variables Z0, Z1, Z2, ···, Znby

then the conditional probabilities

for k = 1,2,···, n, are independent of k. Thus the matrix of transition probabilities is
Equilibrium distributions for an open migration process
Authors: Whittle P.
Published: April 2006

We consider a system of colonies in which migration, immigration and emigration take place according to a fairly general rule. Necessary and sufficient conditions for equilibrium are given in the theorem of Section (3). The equilibrium distribution of colony numbers is determined by Equations (7) and (9); the colony sizes are thus statistically independent in equilibrium.

Attention is also paid to the case where one colony becomes a “bottleneck” to circulation, when equilibrium changes character
The finite dam II
Authors: Roes P. B. M.
Published: April 2006

A weir of capacity K is considered in which the water inflow is a process with stationary independent increments. Unless the weir is empty, there is a continuous release of water at unit rate; if K is finite the weir may become full in which case the excess water overflows instantaneously. A weir for which K is infinite will be referred to as infinite dam. For the latter the transient behaviour is well known if the input possesses a second moment (cf. e.g., Prabhu [7]) and serves as the starting point for the present paper. This result is first extended to yield the Laplace transform (L.T.) of the trivariate Laplace-Stieltjes transform (L.S.T.) of the content v(t) at time t, the input X(t) in (0, t) and the total time d(t) in the interval (0, t) during which the dam is dry. (Incidentally, the last two quantities, for relevant time intervals, will be carried throughout.) Then we use a relation between the latter and the L.S.T. of the expected number of downward level y crossings of the v(t) process established in Roes [9]. Since the dam processes considered are Markov processes, we have therewith the L.S.T. of the renewal function of the renewal process imbedded at level y. From this, one finds the L.S.T.'s of first entrance and taboo first entrance times (for their definition see introduction). Next we calculate the first skip times for the infinite dam from the first entrance times and the L.T. of the L.S.T. of v(t). It is then a routine matter to determine the taboo first skip times. From the (taboo) first entrance and skip times we derive the first entrance times for the finite dam, which in turn lead to the renewal functions of the renewal processes imbedded in the finite dam content process v*(t) and hence to the transient behaviour of the finite dam.

The advantage of the present approach over the one given in Roes [8] is that it is entirely probabilistic and avoids involved analytic arguments. As a result, the question of uniqueness of the solution does not arise, while more insight is obtained in the structure. The L.S.T. of several first entrance times and first skip times have been derived by Cohen [2] for compound Poisson input.
Analytic characterization of the optimal control of a queueing system
Authors: Zacks S. , Yadin M.
Published: April 2006

In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.
Epidemics with carriers: A note on a paper of Dietz
Authors: Downton F.
Published: April 2006

In a recent paper Weiss (1965) has suggested a simple model for a carrier-borne epidemic such as typhoid. He considers a population (of size m) of susceptibles into which a number (k) of carriers is introduced. These carriers exhibit no overt symptoms and are only detectable by the discovery of infected persons. He supposed that after the initial introduction of the carriers, the population remains entirely closed and no new carriers arise. The epidemic then progresses until either all the carriers have been traced and isolated or until the entire population has succumbed to the disease.
A necessary condition on minimal cube numberings
Authors: Harper L. H.
Published: April 2006

Let G = (V, E) be a graph with N vertices and A a set of N real numbers. Then a one-to-one mapping ϕ: V → A is called a numbering of G. The elements of A will always be assumed ordered a1 ≦ a2 ≦ … ≦ aN. In [3] and [7] it was shown how to construct numberings of the n-cube, in fact all numberings, which minimize Σe ∈ E Δe where ∆e = |ϕ(v) – ϕ(w)| and e is the edge between vertices v and w. A variant problem of considerable interest is to do the same for Σe ∈ E (Δe)2. It is conjectured that when A = {1,2, …,2n} the natural numbering is the unique minimizer of Σe ∈ E (Δe)2 for every n, but this has so far resisted all efforts. Theorem 1 in the following is the result of attempts to get weaker results, namely to thin out the ranks of those numberings which could possibly minimize Σe ∈ E (Δe)2. The second problem posed and solved in this paper is a generalization of the results in [3], where the n-cube becomes the n-torus.
Equilibrium distributions for systems of chemical reactions with applications to the theory of molecular adsorption
Authors: Orriss J.
Published: April 2006

In this paper a stochastic model is set up for a certain type of reversible chemical reaction and a solution given for the equilibrium distribution; this solution is then extended to deal with any system of chemical reactions.

Three different types of reaction are considered:

(1) Several substances Ai react together and give a set of substances Bj. The reaction is reversible, with the substances Ai appearing only on one side of the reaction equation and the substances Bj only on the other.

(2) Several different reactions involving the substances Ai and Bj take place simultaneously, but in each reaction equation the substances Ai can appear only on one side and the Bj only on the other.

(3) The restriction of the sets Ai and Bj to different sides of the reaction equations is removed: any reaction involving any of the substances Aiand Bj on either side of the equation is permissible.

The paper concludes with some applications of the results to problems of molecular adsorption.
Asymptotic correlation in a queue
Authors: Craven B. D.
Published: April 2006

Let Xt denote the waiting time of customer t in a stationary GI/G/1 queue, with traffic intensity τ; let ρn denote the correlation between Xt and Xt+n. For a rational GI/G/1 queue, in which the distribution of the difference between arrival and service intervals has a rational characteristic function, it is shown that, for large n, ρn is asymptotically proportional to n–3/2e–βn, where β and the factor of proportionality are calculable. The asymptotic law n–3/2e–βn applies also to the approach of the waiting-time distribution to the stationary state in an initially empty rational GI/G/1 queue, and to the correlations in the queueing systems recently analysed by Cohen [1]. Its more general applicability is discussed.
An optimal isolation policy for an epidemic
Authors: Abakuks Andris
Published: April 2006

Policies of isolating infectives in the general stochastic epidemic are considered. With costs assigned to the infection and isolation of individuals, an optimal policy is found, which at any stage minimises the expected future cost. An optimal policy is also found for the general deterministic epidemic and the two policies are compared. Finally, some numerical examples are provided.
Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary
Authors: Paranjape S. R. , Park C.
Published: April 2006

Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.
Weak convergence in an appointment system
Authors: Anderson C. W.
Published: April 2006

It is assumed that customers at a service facility have appointments at times 0,1,2, … for which they may be unpunctual by random amounts or may never arrive at all. A weak convergence theorem is proved for the process which counts the number of arrivals. This makes it possible to carry over the results of Iglehart and Whitt (1970a) to obtain heavy traffic functional limit theorems for queues with arrivals by appointment.
The asymptotic theory of linear time-series models
Authors: Hannan E. J.
Published: April 2006

A linear time-series model is considered to be one for which a stationary time series, which is purely non-deterministic, has the best linear predictor equal to the best predictor. A general inferential theory is constructed for such models and various estimation procedures are shown to be equivalent. The treatment is considerably more general than previous treatments. The case where the series has mean which is a linear function of very general kinds of regressor variables is also discussed and a rather general form of central limit theorem for regression is proved. The central limit results depend upon forms of the central limit theorem for martingales.
Non-linear regression for multiple time-series
Authors: Robinson P. M.
Published: April 2006

A general multivariate non-linear regression model is considered, including as special cases linear regression when the regression matrix is of less than full rank, simultaneous equations systems and regression on an unobservable predetermined variable. Given a time-series of observations at unit intervals we consider the estimation of the parameters, subject to non-linear constraints, by minimizing a criterion based on the Fourier-transformed model. We allow the residuals to be generated by a stationary, linear, process and establish asymptotic properties of our estimates.
The optimal admission policy to a multiserver queue with finite horizon
Authors: Emmons H.
Published: April 2006

An M/M/s queueing system with a simple cost structure is considered, under the assumption that the system will close in a finite time after which any remaining customers will require extra overtime service costs. We determine the optimal policy for admitting customers to the queue, as a function of the time, t, to closing and the current queue length, i. It is shown to have the form: admit if and only if f1(t) ≦ i ≦ f2(t). The bounds f1(t) and f2(t) are specified, and it is shown under what conditions f1(t) = 0 (a control limit rule) or f2(t) = ∞ (an inverse control limit rule).
Some asymptotic results on multiple matching
Authors: Hafner R. , Sendler W.
Published: April 2006

We consider s ≦ n randomly chosen permutations of the numbers 1, 2, …, n, and write them under each other, thus forming an s × n matrix, called “random-batch”. A rule, prescribing how many elements of a column may occur exactly one time, how many may occur exactly two times, etc., is called a fixpoint-structure. Assuming each possible permutation to be chosen with equal probability, the number of columns having a certain fixpoint-structure F is a random variable X(F). The limiting distribution of X(F) for n→ ∞ is considered for different cases of s = s(n). The main result (Theorem 4) says, that the common distribution of a finite number t of given fixpoint-structures tends to the product of t Poisson-laws, n→ ∞.
Characterizations of the exponential distribution by order statistics
Authors: Huang J. S.
Published: April 2006

Let X1,n ≦ … ≦ Xn, n be the order statistics of a sample of size n from a distribution function F. Desu (1971) showed that if for all n ≧ 2, nX1,n is identically distributed as X1, 1, then F is the exponential distribution (or else F degenerates). The purpose of this note is to point out that special cases of known characterization theorems already constitute an improvement over this result. We show that the characterization is preserved if “identically distributed” is weakened to “having identical (finite) expectation”, and “for all n ≧ 2” is weakened to “for a sequence of n's with divergent sum of reciprocals”.
The candidate problem with unknown population size
Authors: Rasmussen Will T. , Robbins Herbert
Published: April 2006

The familiar problem of maximizing the probability of choosing the best from a group of N candidates, where N is known, is extended to the case of N unknown. An a priori distribution is assumed for N, and the case of a uniform distribution is examined. Let VN denote the probability of choosing the best from a group of at most N candidates, then it is shown that limN→∞VN = 2e–2.
Time-reversibility of linear stochastic processes
Authors: Weiss Gideon
Published: April 2006

Time-reversibility is defined for a process X(t) as the property that {X(t1), …, X(tn)} and {X(– t1), …, X(– tn)} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes.
Relations between queue-size and waiting-time distributions
Authors: Mori Masao
Published: April 2006

Two types of representations for relation between queue-size and waiting-time distributions are studied. By using these, an incomplete but conceptually nice generalization of Pollaczek–Khinchine formula for mean waiting time for M/G/c is obtained.
A note on the extinction rates of some birth–death processes
Authors: Bramson Maury , Griffeath David
Published: April 2006

In this note we are concerned with the rate of extinction of certain continuous-time birth-death processes on the positive integers with absorption at 0. The class we deal with includes birth-death processes with mean holding time h(i) at i such that h (i)∼ i–α as i →∞, 0 ≦ α< 1. In general, our result estimates to within a constant multiple the probability of non-extinction by time t. For h(i)∼ i–α, the result states that the probability of non-extinction is of order t−1/(2-α) We give an application to interacting particle systems.
On a Markovian queue with weakly correlated interarrival times
Authors: Latouche Guy
Published: April 2006

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated.

The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.
The moment ratios of particle size distributions in some simple growth models
Authors: MacGillivray H. L.
Published: April 2006

Important parameters of particle size distributions in dispersed systems in engineering and related fields are ratios of moments and inverse powers of these ratios, known as mean sizes. The variation in these parameters is examined for the simplest growth model in which the size distribution is translated, and the results for this process considered in relation to the problems of models of other growth processes. For initial size distributions with monotone hazard rate, the results are particularly significant, and the properties of the normalised moments of other distributions are also considered.
On the maximum and absorption time of left-continuous random walk
Authors: Pakes Anthony G.
Published: April 2006

In a recent paper Green (1976) obtained some conditional limit theorems for the absorption time of left-continuous random walk. His methods require that in the driftless case the increment distribution has exponentially decreasing tails and that the same is true for a transformed distribution in the case of negative drift.

Here we take a different approach which will produce Green's results under minimal conditions. Limit theorems are given for the maximum as the initial position of the random walk tends to infinity.
Random sequential packing in Euclidean spaces of dimensions three and four and a conjecture of Palásti
Authors: Blaisdell B. Edwin , Solomon Herbert
Published: April 2006

A conjecture of Palásti [11] that the limiting packing density β d in a space of dimension d equals β d where ß is the limiting packing density in one dimension continues to be studied, but with inconsistent results. Some recent correspondence in this journal [7], [8], [13], [14], [15], [16], [18], [19], [20] as well as some other papers indicate a lively interest in the subject. In a prior study [3], we demonstrated that the conjectured value in two dimensions was smaller than the actual density. Here we demonstrate that this is also so in three and four dimensions and that the discrepancy increases with dimension.
First-passage times for the partial sums of a sequence of geometric distributions
Authors: Woods A. J.
Published: April 2006

It is shown here that questions about the probability distributions of the partial sums of a sequence of geometric distributions, all with different parameters, can be answered by considering the transition probabilities of a homogeneous Markov chain. The result is applied to the embedded random walk of an epidemic process.
Coverage problems and random convex hulls
Authors: Jewell Nicholas P. , Romano Joseph P.
Published: April 2006

Consider the placement of a finite number of arcs on the circle of circumference 2π where the midpoint and length of each arc follows an arbitrary bivariate distribution. In the case where each arc has lengthπ, the probability that the circle is completely covered is equal to the probability that the convex hull of a finite random sample of points, chosen according to a certain bivariate distribution in the plane contains the origin. In general, we show that evaluating the probability that the random convex hull contains a fixed disc is equivalent to solving the general coverage problem where the midpoint and length of each arc follows an arbitrary bivariate distribution. Exact formulae for the above probabilities are obtained and some examples are considered.
A counterexample to a conjecture on optimal list ordering
Authors: Anderson E. J. , Nash P. , Weber R. R.
Published: April 2006

A number of items are arranged in a line. At each unit of time one of the items is requested, the i th being requested with probability Pi. We consider rules which reorder the items between successive requests in a fashion which depends only on the position in which the most recently requested item was found. It has been conjectured that the rule which always moves the requested item one closer to the front of the line minimizes the average position of the requested item. An example with six items shows that the conjecture is false.
Kac's formula, levy's local time and brownian excursion
Authors: Louchard G.
Published: April 2006

Kac's formula for Brownian functionals and Levy's local time decomposition are shown to be useful tools in analysing Brownian excursion properties. These tools are applied to maximum, local time and area distributions. Some curious connections between some of these distributions are explained by simple probabilistic arguments.
Estimation for diffusion processes under misspecified models
Authors: McKeague Ian W.
Published: April 2006

The asymptotic behavior of the maximum likelihood estimator of a parameter in the drift term of a stationary ergodic diffusion process is studied under conditions in which the true drift function and true noise function do not coincide with those specified by the parametric model.
Mean and variance of vacancy for distribution of k-dimensional spheres within k-dimensional space
Authors: Hall Peter
Published: April 2006

Let n points be distributed independently within a k-dimensional unit cube according to density f. At each point, construct a k-dimensional sphere of content an. Let V denote the vacancy, or ‘volume' not covered by the spheres. We derive asymptotic formulae for the mean and variance of V, as n → ∞and an → 0. The formulae separate naturally into three cases, corresponding to nan → 0, nan → a (0 < a <∞) and nan →∞, respectively. We apply the formulae to derive necessary and sufficient conditions for V/E(V) → 1 in L2.
Some sufficient conditions for non-ergodicity of markov chains
Authors: Szpankowski Wojciech
Published: April 2006

Some sufficient conditions for non-ergodicity are given for a Markov chain with denumerable state space. These conditions generalize Foster's results, in that unbounded Lyapunov functions are considered. Our criteria directly extend the conditions obtained in Kaplan (1979), in the sense that a class of Lyapunov functions is studied. Applications are presented through some examples; in particular, sufficient conditions for non-ergodicity of a multidimensional Markov chain are given.
On the comparison of point processes
Authors: Deng Y. L.
Published: April 2006

Several different orderings for the comparison of point processes have been introduced and their relationships discussed in Whitt [9], Daley [2] and Deng [4]. It is of some interest to know whether these orderings, in general, are preserved under various operations on point processes. Some results concerning limit operations were given in Deng [4].

In the present paper, we first further introduce some convex and concave orderings for counting processes, and survey the relationships among all orderings mentioned in [9], [4] and this paper. Then we focus our attention on the study of the conditions for the preservation of orderings under the operations of superposition, thinning, shift, and random change of time.
A full-information best-choice problem with finite memory
Authors: Tamaki Mitsushi
Published: April 2006

n i.i.d. random variables with known continuous distribution are observed sequentially with the objective of selecting the largest. This paper considers the finite-memory case which, at each stage, allows a solicitation of anyone of the last m observations as well as of the present one. If the (k – t)th observation with value x is solicited at the k th stage, the probability of successful solicitation is p1(x) or p2(x) according to whether t = 0 or 1 ≦ t ≦ m. The optimal procedure is shown to be characterized by the double sequences of decision numbers. A simple algorithm for calculating the decision numbers and the probability of selecting the largest is obtained in a special case.
Bounding the stochastic performance of continuum structure functions. II
Authors: Baxter Laurence A. , Kim Chul
Published: April 2006

A continuum structure function γ is a non-decreasing mapping from the unit hypercube to the unit interval. Block and Savits (1984) use the sets and to determine bounds on the distribution of γ (X) when X is a vector of associated random variables. It is shown that, if γ admits of a modular decomposition, improved bounds may be obtained.
The impact of the composition of the customer base in general queueing models
Authors: Federgruen A. , Groenevelt H.
Published: April 2006

We consider general queueing models dealing with multiple classes of customers and address the question under what conditions and in what (stochastic) sense the marginal increase in various performance measures, resulting from the addition of a new class of customers to an existing system, is larger than if the same class were added to a system dealing with only a subset of its current customer base.

Our results enhance our understanding of the dependence of various performance measures with respect to the composition of the customer base. In addition they translate readily into convexity results in an (appropriately defined) arrival rate.
Periodic and sequential preventive maintenance policies
Authors: Nakagawa Toshio
Published: April 2006

This paper considers periodic and sequential preventive maintenance (PM) policies for the system with minimal repair at failure: the PM is done (i) at periodic times kx and (ii) at constant intervals xk (k = 1, 2, ···, N). The system has a different failure distribution between PM'S and is replaced at the Nth PM. The optimal policies which minimize the expected cost rates are discussed. The optimal x and N of periodic PM and {xk} of sequential PM are easily computed in a Weibull distribution case.