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Glinus is a small genus of Molluginaceae with 8–10 species mostly distributed in the tropics of the World. Its composition and evolutionary relationships were poorly studied. A new molecular phylogeny constructed here using nuclear (ITS) and chloroplast (rbcL, trnK-matK) markers confirmed the monophyly of the genus. Based on ITS analysis, the following well-supported lineages are present within Glinus: the G. bainesii lineage is recovered as sister to the remainder of the genus followed by G. oppositifolius. Three other clades are: G. hirtus with G. orygioides; G. radiatus and G. lotoides; the latter is represented by a sample from North America, and G. zambesiacus as sister to G. setiflorus + G. lotoides + G. dictamnoides. On the plastid gene tree, G. bainesii + G. oppositifolius form a sister clade to all other Glinus species. The next clade is formed by G. hirtus and G. orygioides followed by G. radiatus plus an American sample of G. lotoides. The next branch comprises G. setiflorus as sister to G. zambesiacus + G. lotoides + G. dictamnoides. Glinus seems to have originated from Africa around the Late Eocene or Early Miocene, with further radiations to Australia and the Americas during the Late Miocene or Late Pliocene. Compared with the previous limited character set used for the diagnostics, we have found ten new morphological and carpological traits distinguishing Glinus members. In both trees based on nuclear and plastid datasets, the major phylogenetic clades cannot be characterized by the peculiar morphological characters. Many shared character states leading to their contrasting pattern in the multivariate analysis model are interpreted as a high homoplasy in the phylogenetically distant species. We paid special attention to the composition of the genus in Sub-Saharan Africa, a region with the greatest species diversity. Our results provide new insight into the taxonomy of Glinus in this region. Glinus lotoides var. virens accepted in many previous works is a synonym of G. dictamnoides that is closely related to G. lotoides based on molecular analysis and morphological characters. The status of the American populations of G. lotoides needs further investigation due to different characters of the specimens from the Old and the New World. Many specimens previously identified as G. lotoides var. virens and as the intermediates G. lotoides × G. oppositifolius belong to G. zambesiacussp. nov. and G. hirtuscomb. nov. (≡ Mollugo hirta); the latter species is resurrected from synonymy after 200 years of unacceptance. In some African treatments, G. hirtus was known under the invalidly published name G. dahomensis. Glinus zambesiacus is distributed in the southern and eastern parts of tropical Africa, and G. hirtus previously assumed to be endemic to West Africa is indeed a species with a wide distribution across the tropical part of the continent. Glinus microphyllus previously accepted as endemic to West Tropical Africa together with other new synonyms (G. oppositifolius var. lanatus, G. herniarioides, Wycliffea rotundifolia) is considered here as G. oppositifolius var. keenaniicomb. nov. (≡ Mollugo hirta var. keenanii), a variety found across the entire distribution of G. oppositifolius (Australia, Asia, and Africa). The presence of the American G. radiatus in Africa is not confirmed, and all records of this species belong to G. hirtus. The lectotypes of some names (G. dictamnoides, G. herniarioides, Mollugo hirta, M. setiflora, Pharnaceum pentagynum, Wycliffea) as well as a neotype of G. trianthemoides are designated. A new key to the identification of all Glinus species in Sub-Saharan Africa is provided. A checklist is given of all accepted species in this region (G. bainesii, G. hirtus, G. lotoides, G. oppositifolius s.l., G. setiflorus, and G. zambesiacus) with their nomenclature, morphological description and geographical distribution.

We show that $$\begin{equation*}\sum_{\substack{p_n\le x\\ p_{n+1}-p_n\ge\sqrt{p_n}}}(p_{n+1}-p_n) \ll_{\varepsilon} x^{3/5+\varepsilon}\end{equation*}$$or any fixed $\varepsilon>0$. This improves a result of Matomäki, in which the exponent was $2/3$.

We develop a version of Ekedahl's geometric sieve for integral quadratic forms of rank at least five. As one ranges over the zeros of such quadratic forms, we use the sieve to compute the density of coprime values of polynomials, and furthermore, to address a question about local solubility in families of varieties parameterised by the zeros., 29 pages

Perceptions about the ability of alien species to provide superior ecosystem services over the native species have motivated their importation and distribution across the world. While these species may be providing goods and services, some have now escaped the area of their introduction and invaded other ecosystems posing a threat to biodiversity and ecosystem services. Invasion by alien species threaten achievement of Sustainable Development Goal 2 (food security), 6 (water availability), 12 (sustainable consumption and production patterns) and 15 (protecting ecosystems and forests). This article discusses the potential impact of terrestrial invasive plant, Prosopis juliflora and aquatic weed, Salvinia molesta on ecosystem services in Botswana. Information for this study was collected by review of academic journal articles on the invasiveness of P. juliflora and S. molesta and their impacts on ecosystem services in Africa and other developing countries. The literature review has shown that P. juliflora has the potential to lower water table in water-limited ecosystems, resulting in negative impacts on biodiversity and ecosystem services. In some countries P. julifolia inhibits growth of keystone species hindering their capacity to provide services. A Salvinia molesta invasion in the Okavango Delta, Botswana, has the potential to decrease ecosystem services. It will, thus, impact negatively on the welfare of the riparian communities who depend on fishing and tourist-related activities for their livelihoods. The review contributes towards understanding of the impacts of terrestrial and aquatic invasive plant species on ecosystem services, and importance of biodiversity and ecosystem services in achievement of Sustainable Development Goals. The review further recommends quantifiable monetary assessment of the services delivered by different ecosystems. Such assessment provides information on the value of ecosystem services and can yield information on how much is lost due to invasion by alien plant species.

We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refines the well known result of Chen., 22 pages; errors with numerical calculations corrected after referee report; main result somewhat improved

Let k be an algebraic closure of k. In the case when P(t) has at most one root in k, the open subset of the affine variety (1) given by P(t)y~O is a principal homogeneous space under an algebraic k-torus. In this case it is well known that the Brauer Manin obstruction is the only obstruction to the Hasse principle and weak approximation on any smooth projective model of this variety (Colliot-Th~l~ne and Sansuc [CSanl]). In this paper we prove the same result when P(t) has exactly two roots in k and no other roots in k, and k is the field of rational numbers Q. An immediate change of variables then reduces (1) to the equation ta~

We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals. The bounds are uniform in the curve and involve the rank of the corresponding Jacobian. The method used in the proof is a combination of the “determinant method” with an m-descent on the curve.

Angiotensin II AT 1 receptor blockers have been introduced into clinical practice; however, larger-scale information on their tolerability and effects on renal function in patients with hypertension and renal insufficiency is limited. A 6-month, double-masked, placebo-controlled, multicenter, clinical trial was performed to address this issue. Fifty-six adults with hypertension and reduced renal function were studied. They received the AT 1 receptor blocker valsartan (80 mg/d) or placebo, in addition to other antihypertensive drugs. The renal variables studied were glomerular filtration rate, effective renal plasma flow, renal blood flow, serum creatinine level, and 24-hour urinary albumin, protein, and urea excretion. Drug tolerability was also assessed. Differences were not significant between the valsartan and placebo groups with respect to effects on any renal function variable. Furthermore, the tolerability of valsartan and placebo was not different. Compared with placebo, valsartan lowered systolic and diastolic blood pressures. Data from this study suggest that valsartan is well tolerated and effective in treating patients with hypertension and reduced renal function.

Historically, geologic hazards have been primarily identified using high‐resolution 2-D single‐channel seismic (e.g., 3.5 kHz and minisparker records), side‐scan sonar surveys, geotechnical data from selected borings and in‐situ measurements, and drop cores. However, effective use of coherency and other seismic attributes on standard 3-D seismic data can allow early detection and delineation of both surface and subsurface geologic drilling hazards prior to the acquisition of high‐resolution “hazard” surveys.

To compare the antihypertensive efficacy and systemic tolerability of valsartan, a new angiotensin II receptor antagonist, with placebo and with an angiotensin converting enzyme (ACE) inhibitor, enalapril.A total of 348 adult outpatients with mild-to-moderate uncomplicated essential hypertension participated in this double-blind, parallel, study. Patients were allocated randomly in a ratio of 2:2:1 to receive 80 mg valsartan once a day, 20 mg enalapril once a day, or placebo for 8 weeks in general practice. Patients were assessed at 4 and 8 weeks of therapy.The primary efficacy variable was the change from baseline in mean sitting diastolic blood pressure (SDBP) after 8 weeks of therapy. Secondary variables included the change in sitting systolic blood pressure (SSBP) and response rates at 8 weeks.Valsartan and enalapril produced statistically significant reductions in diastolic and systolic blood pressures compared with placebo. Similar falls were found in both of the active treatment groups with mean changes in SDBP at 8 weeks of -9.5 mmHg for valsartan and -9.4 mmHg for enalapril (-4.5 mmHg for placebo). No significant differences between valsartan and enalapril were found for reductions in SDBP or SSBP. Response rates at 8 weeks were significantly greater for valsartan (54%) and enalapril (58%) than for placebo (20%), with no significant difference between the two active treatments. Both valsartan and enalapril demonstrated a consistent antihypertensive effect over time, with 90% of patients with a response at 4 weeks responding at 8 weeks. Both of the treatments were tolerated well. Although the incidence of coughing was generally low in the study, more cases were reported with enalapril (three) than with valsartan (one) or placebo (none).The data show 80 mg valsartan once a day to be as effective as 20 mg enalapril once a day in the treatment of mild-to-moderate hypertension. Valsartan is tolerated well and does not appear to be associated with any increase in the incidence of coughing.

We discuss connections between analytic number theory and geometry of higher-dimensional algebraic varieties.

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in International Mathematics Research Notices. The definitive publisher-authenticated version William D. Banks, Roger Heath-Brown and Igor E. Shparlinski, On the average value of divisor sums in arithmetic progressions, Int Math Res Notices 2005 (1): 1-25, is available online at: http://imrn.oxfordjournals.org/content/2005/1/1.abstract. doi: 10.1155/IMRN.2005.1. © 2005 Hindawi Publishing Corporation.

Roger Heath-Brown (37) is a Reader in Pure Mathematics at Oxford University, and a Tutorial Fellow at Magdalen College. He works in analytic number theory, with interests covering the distribution of prime numbers, Waring's problem and Fermat's Last TheoremThis term I'm giving a first year lecture course—Groups, Rings and Fields. I'm not at my best at 9 am and despite my efforts the undergraduates find me rather dull. The weaker ones have to have everything spelled out in full, with the result that the interesting things are too sparsely scattered for the stronger students. I'm back in college by 10.30 am having collected a pile of mail. There's a request from the Mathematical Gazette for a “day in the life of” style article, and I toy with the idea of describing an occasion on which a journal asks me to describe a typical day's work …. I also receive a referee's report on a paper submitted to me as an editorial advisor to the London Mathematical Society. The report is not encouraging and I reject the paper—a frequent enough duty, but not one I relish. The associated paperwork fills the next three-quarters of an hour. This particular manuscript is rather too similar to something published in 1963. While double-checking this in “Reviews in Number Theory” I notice an abstract of a quite unrelated paper, by a Finnish mathematician.

The object of this paper is to present new proofs of the classical ternary theorems of additive prime number theory. Of these the best known is Vinogradov's result on the representation of odd numbers as the sums of three primes; other results will be discussed later. Earlier treatments of these problems used the Hardy-Littlewood circle method, and are highly analytical. In contrast, the method we use here is a (technically) elementary deduction from the Siegel-Walfisz Prime Number Theory. It uses ideas from Linnik's dispersion method, together with Vaughan's identity.