Some identities for Jacobsthal and Jacobsthal-Lucas numbers satisfying higher order recurrence relations

The Jacobsthal recurrence relation is extended to higher order recurrence relations and the basic list of identities provided by A. F. Horadam [10] is expanded and extended to several identities for some of the higher order cases. Keywords: sequences, recurrence relation

AN EXTENSION OF SOME RESULTS DUE TO JARDEN

This paper defines some generalized Fibonacci and Lucas sequences which satisfy arbitrary order linear recurrence relations and which answer a problem posed by Jarden in 1966 about generalizing an elegant result for a connection between even and odd subscripted Fibonacci and Lucas numbers

Some aspects of Fibonacci polynomial congruences

This paper formulates a definition of Fibonacci polynomials which is slightly different from the traditional definitions, but which is related to the classical polynomials of Bernoulli, Euler and Hermite. Some related congruence properties are developed and some unanswered questions are outlined. Keywords: Congruences, recurrence relations, Fibonacci sequence, Lucas sequences, umbral calculus

ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS

The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to generalized continued fractions with matrices as the unifying elements

A systematic review of the use of an expertise-based randomised controlled trial design

Acknowledgements JAC held a Medical Research Council UK methodology (G1002292) fellowship, which supported this research. The Health Services Research Unit, Institute of Applied Health Sciences (University of Aberdeen), is core-funded by the Chief Scientist Office of the Scottish Government Health and Social Care Directorates. Views express are those of the authors and do not necessarily reflect the views of the funders.Peer reviewedPublisher PD

U.S. Fresh Fruit and Vegetable Marketing: Emerging Trade Practices, Trends, and Issues

In the past year, trade practices between fresh produce shippers and food retailers gained national attention. Shippers are concerned that recent retail consolidation has led to market power and the growing incidence of fees and services. Retailers argue that these new trade practices reflect their costs of doing business and the demands of consumers. Trade practices include fees such as volume discounts and slotting fees, as well as services like automatic inventory replenishment, special packaging, and requirements for third-party food safety certification. Trade practices also refer to the overall structure of a transaction-for example, long-term relationships or contracts versus daily sales with no continuing commitment. This study compares trade practices in 1999 with those prevalent in 1994, placing them in the broader context of the evolving shipper/retailer relationship. Most shippers and retailers reported that the incidence and magnitude of fees and services associated with transactions has increased over the last 5 years. Fees paid to retailers are usually around 1-2 percent of sales for most of the commodities we examined, but 1-8 percent for bagged salads. Information on the incidence and magnitude of these new practices is scarce. To augment information that is publicly available, we interviewed a limited number of shippers, retailers, and wholesalers about their firms and trade practices. We received a high level of voluntary cooperation from the interviewed firms.produce, fresh fruit and vegetables, fresh-cut produce, trade practices, fees and services, slotting fees, retail consolidation, produce shipper consolidation, Crop Production/Industries, Marketing,

Greater Sage-Grouse Resource Selection Drives Reproductive Fitness Under a Conifer Removal Strategy

The link between individual variation in resource selection (e.g., functional response) and fitness creates a foundation for understanding wildlife-habitat relationships. Although many anthropogenic activities adversely affect these relationships, it is largely unknown whether projects implemented to benefit wildlife populations actually achieve this outcome. For sagebrush (Artemisia spp.) obligate species such as the greater sage-grouse (Centrocercus urophasianus; sage-grouse), expansion of juniper (Juniperus spp.) and pinyon-pine (Pinus spp.; conifers) woodlands into sagebrush ecosystems has been identified as a conservation threat. This threat is intensified when a sagebrush ecosystem is bounded by naturally unsuitable habitats. As such, federal, state, and private land managers have implemented landscape-level management to remove conifers on thousands of hectares of sagebrush habitat across the western United States. Despite the scale of contemporary conifer treatments, little was previously known whether sage-grouse will occupy these manipulated landscapes and whether occupancy has consequences on fitness components. To address these questions, we monitored nest and brood success rates for 96 radio-marked sage-grouse from 2012-2015 that inhabited conifer-dominated landscapes in the Box Elder Sage-grouse Management Area in Utah where mechanical conifer removal projects were completed. We then linked sage-grouse resource selection to individual nest (n = 95) and brood (n = 56) success by incorporating random-slope Resource Selection Functions as explanatory predictors in a logistic brood success model. Using the novel approach of random slope covariates, we demonstrated that sage-grouse selected for nest and brooding sites closer to conifer removal areas and that the probability of individual nest and brood success declined (β = − 0.10 and β = − 0.74, respectively) as sage-grouse females selected sites farther from conifer removal areas. Our research provided the first evidence that mechanical conifer removal treatments can increase suitable available breeding habitats for female sage-grouse and that individuals who occupied these areas experienced enhanced nest and brood success

An EIAV field isolate reveals much higher levels of subtype variability than currently reported for the equine lentivirus family

<p>Abstract</p> <p>Background</p> <p>Equine infectious anemia virus (EIAV), a lentivirus that infects horses, has been utilized as an animal model for the study of HIV. Furthermore, the disease associated with the equine lentivirus poses a significant challenge to veterinary medicine around the world. As with all lentiviruses, EIAV has been shown to have a high propensity for genomic sequence and antigenic variation, especially in its envelope (Env) proteins. Recent studies have demonstrated Env variation to be a major determinant of vaccine efficacy, emphasizing the importance of defining natural variation among field isolates of EIAV. To date, however, published EIAV sequences have been reported only for cell-adapted strains of virus, predominantly derived from a single primary virus isolate, EIAV_Wyoming(EIAV_WY).</p> <p>Results</p> <p>We present here the first characterization of the Env protein of a natural primary isolate from Pennsylvania (EIAV_PA) since the widely utilized and referenced EIAV_WYstrain. The data demonstrated that the level of EIAV_PAEnv amino acid sequence variation, approximately 40% as compared to EIAV_WY, is much greater than current perceptions or published reports of natural EIAV variation between field isolates. This variation did not appear to give rise to changes in the predicted secondary structure of the proteins. While the EIAV_PAEnv was serologically cross reactive with the Env proteins of the cell-adapted reference strain, EIAV_PV(derivative of EIAV_WY), the two variant Envs were shown to lack any cross neutralization by immune serum from horses infected with the respective virus strains.</p> <p>Conclusion</p> <p>Taking into account the significance of serum neutralization to universal vaccine efficacy, these findings are crucial considerations towards successful EIAV vaccine development and the potential inclusion of field isolate Envs in vaccine candidates.</p

Envelope determinants of equine lentiviral vaccine protection

Lentiviral envelope (Env) antigenic variation and associated immune evasion present major obstacles to vaccine development. The concept that Env is a critical determinant for vaccine efficacy is well accepted, however defined correlates of protection associated with Env variation have yet to be determined. We reported an attenuated equine infectious anemia virus (EIAV) vaccine study that directly examined the effect of lentiviral Env sequence variation on vaccine efficacy. The study identified a significant, inverse, linear correlation between vaccine efficacy and increasing divergence of the challenge virus Env gp90 protein compared to the vaccine virus gp90. The report demonstrated approximately 100% protection of immunized ponies from disease after challenge by virus with a homologous gp90 (EV0), and roughly 40% protection against challenge by virus (EV13) with a gp90 13% divergent from the vaccine strain. In the current study we examine whether the protection observed when challenging with the EV0 strain could be conferred to animals via chimeric challenge viruses between the EV0 and EV13 strains, allowing for mapping of protection to specific Env sequences. Viruses containing the EV13 proviral backbone and selected domains of the EV0 gp90 were constructed and in vitro and in vivo infectivity examined. Vaccine efficacy studies indicated that homology between the vaccine strain gp90 and the N-terminus of the challenge strain gp90 was capable of inducing immunity that resulted in significantly lower levels of post-challenge virus and significantly delayed the onset of disease. However, a homologous N-terminal region alone inserted in the EV13 backbone could not impart the 100% protection observed with the EV0 strain. Data presented here denote the complicated and potentially contradictory relationship between in vitro virulence and in vivo pathogenicity. The study highlights the importance of structural conformation for immunogens and emphasizes the need for antibody binding, not neutralizing, assays that correlate with vaccine protection