Type 1 and 2 sets for series of translates of functions

Suppose Lambda is a discrete infinite set of nonnegative real numbers. We say that Lambda is type 1 if the series s(x)=Sigma lambda is an element of Lambda f(x+lambda) satisfies a zero-one law. This means that for any non-negative measurable f:R ->[0,+infinity) either the convergence set C(f,Lambda)={x:s(x)<+infinity}=R modulo sets of Lebesgue zero, or its complement the divergence set D(f,Lambda)={x:s(x)=+infinity}=R modulo sets of measure zero. If Lambda is not type 1 we say that Lambda is type 2.The exact characterization of type 1 and type 2 sets is not known. In this paper we continue our study of the properties of type 1 and 2 sets. We discuss sub and supersets of type 1 and 2 sets and give a complete and simple characterization of a subclass of dyadic type 1 sets. We discuss the existence of type 1 sets containing infinitely many elements independent over the rationals. Finally, we consider unions and Minkowski sums of type 1 and 2 sets

Random constructions for translates of non-negative functions

Suppose A is a discrete infinite set of nonnegative real numbers. We say that A is type 2 if the series s(x) = Sigma lambda Lambda f (x + lambda) does not satisfy a zero-one law. This means that we can find a non-negative measurable "witness function" f : R -> [0,+ infinity) such that both the convergence set C(f, Lambda) ={x : s(x) < + infinity} and its complement the divergence set D (f, Lambda) = {x : s(x) = +infinity} are of positive Lebesgue measure. If Lambda is not type 2 we say that A is type 1. The main result of our paper answers a question raised by Z. Buczolich, J-P. Kahane, and D. Mauldin. By a random construction we show that one can always choose a witness function which is the characteristic function of a measurable set. We also consider the effect on the type of a set A if we randomly delete its elements. Motivated by results concerning weighted sums Sigma c(n)f(nx)and the Khinchin conjecture, we also discuss some results about weighted sum

Avaliação de fontes integradas de nutrientes no solo dos parâmetros de crescimento e produção de sorgo no solo de Makurdi, Nigéria

Research was carried out at University Commercial Crop Farm, Federal University of Agriculture Makurdi, to evaluate the effects of different soil nutrient sources on the growth and yield of sorghum in the 2016 and 2017 cropping season under rain-fed condition. The experiment consisted of fourteen treatments; (I) Control, (II) Soybean intercrop, (III) 2.0 t/ha-1 of PM, (IV) 2.0 t/ha-1 of PM + Soybean, (V) 3.5 t/ha-1 of PM, (VI) 3.5 t/ha-1 of PM + Soybean, (VII) 0.2 t/ha-1 of CP, (VIII) 0.2 t/ha-1 of CP + Soybean, (IX) 0.4 t/ha-1 of CP, (X) 0.4 t/ha-1 of CP + Soybean, (XI) 30 kg N/ha-1, (XII) 30 kg N/ha-1 + Soybean, (XIII) 60 kg N/ha-1, and (XIV) 60 kg N/ha-1 + Soybean. The experiment was laid in Randomised Complete Block Design in three (3) replications. Sole applications of compost manure at 0.4 t/ha-1 had significant difference on leaf area. Soybean as nutrient source did not have significant difference on crop parameters. Poultry manure, NPK fertilizer and compost manure significantly affected growth and yield parameters in the two cropping seasons. The highest yield were obtained from application of NPK fertilizer at 60 kg N/ha-1 in plots where sorghum was intercropped with soybeans, this was not however significant when compared with plots where NPK fertilizer was applied without soybean mixture.La investigación se llevó a cabo en la Granja de Cultivos Comerciales de la Universidad, Universidade Federal de Agricultura Makurdi, para evaluar los efectos de diferentes fuentes de nutrientes del suelo sobre el crecimiento y el rendimiento del sorgo en las temporadas 2016 y 2017 bajo condiciones de secano. El experimento constó de catorce tratamientos; (I) Control, (II) Soja intercalado, (III) 2,0 t/ha-1 PM, (IV) 2,0 t/ha-1 PM + Soja, (V) 3,5 t/ha-1 de PM, (VI) 3,5 t/ha-1 de PM + Soja, (VII) 0,2 t/ha-1 de PB, (VIII) 0,2 t/ha-1 de PB + Soja, (IX) 0,4 t/ha-1 de PB, ( X) 0,4 t/ha-1 de PB + Soja, (XI) 30 kg N/ha-1, (XII) 30 kg N/ha-1 + Soja, (XIII) 60 kg N/ha-1, y ( XIV) 60 kg N/ha-1 + Soja. El experimento se colocó en un diseño aleatorio de bloques completos en tres (3) repeticiones. Aplicaciones aisladas de compost de estiércol a una dosis de 0,4 t/ha-1 tuvieron una diferencia significativa en el área foliar. La soja como fuente de nutrientes no mostró diferencias significativas en los parámetros de cultivo. El estiércol de pollo, el fertilizante NPK y el estiércol de compost afectaron significativamente los parámetros de crecimiento y rendimiento en ambas temporadas. Los mayores rendimientos se obtuvieron con la aplicación de fertilizante NPK a la dosis de 60 kg N/ha-1 en las parcelas donde se intercaló sorgo con soya, pero no fue significativo al compararlo con las parcelas donde se aplicó fertilizante NPK sin mezcla de soya. .A pesquisa foi realizada na University Commercial Crop Farm, Universidade Federal de Agricultura Makurdi, para avaliar os efeitos de diferentes fontes de nutrientes do solo no crescimento e rendimento do sorgo na safra de 2016 e 2017 sob condições de sequeiro. O experimento constou de quatorze tratamentos; (I) Controle, (II) Consórcio de soja, (III) 2,0 t/ha-1 de PM, (IV) 2,0 t/ha-1 de PM + Soja, (V) 3,5 t/ha-1 de PM, (VI) 3,5 t/ha-1 de PM + Soja, (VII) 0,2 t/ha-1 de PB, (VIII) 0,2 t/ha-1 de PB + Soja, (IX) 0,4 t/ha-1 de PB, (X) 0,4 t/ha-1 de PB + Soja, (XI) 30 kg N/ha-1, (XII) 30 kg N/ha-1 + Soja, (XIII) 60 kg N/ha-1, e (XIV) 60 kg N/ha-1 + Soja. O experimento foi colocado em Design de Bloco Completo Randomizado em três (3) repetições. Aplicações isoladas de esterco de compostagem na dose de 0,4 t/ha-1 tiveram diferença significativa na área foliar. A soja como fonte de nutriente não apresentou diferença significativa nos parâmetros da cultura. O esterco de frango, o fertilizante NPK e o esterco composto afetaram significativamente os parâmetros de crescimento e rendimento nas duas safras. As maiores produtividades foram obtidas com a aplicação do fertilizante NPK na dose de 60 kg N/ha-1 nas parcelas onde o sorgo foi consorciado com a soja, porém não foi significativo quando comparado com as parcelas onde foi aplicado o fertilizante NPK sem mistura de soja

Factors influencing the fracture of nickel-titanium rotary instruments

Abstract Mart|¤ n B, Zelada G, Varela P, Bahillo JG, Maga¤ n F, Ahn S, Rodr|¤ guez C

How large dimension guarantees a given angle

Abstract We study the following two problems: (1) Given n ≥ 2 and α, how large Hausdorff dimension can a compact set A ⊂ R n have if A does not contain three points that form an angle α? (2) Given α and δ, how large Hausdorff dimension can a compact subset A of a Euclidean space have if A does not contain three points that form an angle in the δ-neighborhood of α? Some angles (0, 60 • ) turn out to behave differently than other α ∈ [0, 180 • ]

Expression of the RNA helicase DDX3 and the hypoxia response in breast cancer

&lt;p&gt;Aims: DDX3 is an RNA helicase that has antiapoptotic properties, and promotes proliferation and transformation. In addition, DDX3 was shown to be a direct downstream target of HIF-1α (the master regulatory of the hypoxia response) in breast cancer cell lines. However, the relation between DDX3 and hypoxia has not been addressed in human tumors. In this paper, we studied the relation between DDX3 and the hypoxic responsive proteins in human breast cancer.&lt;/p&gt; &lt;p&gt;Methods and Results: DDX3 expression was investigated by immunohistochemistry in breast cancer in comparison with hypoxia related proteins HIF-1α, GLUT1, CAIX, EGFR, HER2, Akt1, FOXO4, p53, ERα, COMMD1, FER kinase, PIN1, E-cadherin, p21, p27, Transferrin receptor, FOXO3A, c-Met and Notch1. DDX3 was overexpressed in 127 of 366 breast cancer patients, and was correlated with overexpression of HIF-1α and its downstream genes CAIX and GLUT1. Moreover, DDX3 expression correlated with hypoxia-related proteins EGFR, HER2, FOXO4, ERα and c-Met in a HIF-1α dependent fashion, and with COMMD1, FER kinase, Akt1, E-cadherin, TfR and FOXO3A independent of HIF-1α.&lt;/p&gt; &lt;p&gt;Conclusions: In invasive breast cancer, expression of DDX3 was correlated with overexpression of HIF-1α and many other hypoxia related proteins, pointing to a distinct role for DDX3 under hypoxic conditions and supporting the oncogenic role of DDX3 which could have clinical implication for current development of DDX3 inhibitors.&lt;/p&gt

Soil biogeochemistry across Central and South American tropical dry forests

The availability of nitrogen (N) and phosphorus (P) controls the flow of carbon (C) among plants, soils, and the atmosphere, thereby shaping terrestrial ecosystem responses to global change. Soil C, N, and P cycles are linked by drivers operating at multiple spatial and temporal scales: landscape-level variation in macroclimate and soil geochemistry, stand-scale heterogeneity in forest composition, and microbial community dynamics at the soil pore scale. Yet in many biomes, we do not know at which scales most of the biogeochemical variation emerges, nor which processes drive cross-scale feedbacks. Here, we examined the drivers and spatial/temporal scales of variation in soil biogeochemistry across four tropical dry forests spanning steep environmental gradients. To do so, we quantified soil C, N, and P pools, extracellular enzyme activities, and microbial community structure across wet and dry seasons in 16 plots located in Colombia, Costa Rica, Mexico, and Puerto Rico. Soil biogeochemistry exhibited marked heterogeneity across the 16 plots, with total organic C, N, and P pools varying fourfold, and inorganic nutrient pools by an order of magnitude. Most soil characteristics changed more across space (i.e., among sites and plots) than over time (between dry and wet season samplings). We observed stoichiometric decoupling among C, N, and P cycles, which may reflect their divergent biogeochemical drivers. Organic C and N pool sizes were positively correlated with the relative abundance of ectomycorrhizal trees and legumes. By contrast, the distribution of soil P pools was driven by soil geochemistry, with larger inorganic P pools in soils with P-rich parent material. Most earth system models assume that soils within a texture class operate similarly, and ignore subgrid cell variation in soil properties. Here we reveal that soil nutrient pools and fluxes exhibit as much variation among four Neotropical dry forests as is observed across terrestrial ecosystems at the global scale. Soil biogeochemical patterns are driven not only by regional differences in soil parent material and climate, but also by local-scale variation in plant and microbial communities. Thus, the biogeochemical patterns we observed across the Neotropical dry forest biome challenge representation of soil processes in ecosystem models

Association of human cytomegalovirus proteins IRS1 and TRS1 with the viral DNA polymerase accessory subunit UL44

Multiple proteins interacting with DNA polymerases orchestrate DNA replication. Human cytomegalovirus (HCMV) encodes a DNA polymerase that includes the presumptive processivity factor UL44. UL44 is structurally homologous to the eukaryotic DNA polymerase processivity factor proliferating cell nuclear antigen (PCNA), which interacts with numerous proteins. Previous proteomic analysis has identified the HCMV protein IRS1 as a candidate protein interacting with UL44. Nuclease-resistant reciprocal co-immunoprecipitation of UL44 with IRS1 and with TRS1, which has an amino terminus identical to that of IRS1, was observed from lysate of cells infected with viruses expressing epitope-tagged UL44, epitope-tagged IRS1 or epitope-tagged TRS1. Western blotting of protein immunoprecipitated from infected cell lysate indicated that epitope-tagged IRS1 and TRS1 do not associate simultaneously with UL44. Glutathione S-transferase pull-down experiments indicated that IRS1 and TRS1 interact with UL44 via a region that is identical in both proteins. Taken together, these data suggest that IRS1 and TRS1 may compete for association with UL44 and may affect UL44 function differentially

Lakeside Cemeteries in the Sahara: 5000 Years of Holocene Population and Environmental Change

Background: Approximately two hundred human burials were discovered on the edge of a paleolake in Niger that providea uniquely preserved record of human occupation in the Sahara during the Holocene (,8000 B.C.E. to the present). CalledGobero, this suite of closely spaced sites chronicles the rapid pace of biosocial change in the southern Sahara in response tosevere climatic fluctuation.Methodology/Principal Findings: Two main occupational phases are identified that correspond with humid intervals in theearly and mid-Holocene, based on 78 direct AMS radiocarbon dates on human remains, fauna and artifacts, as well as 9 OSLdates on paleodune sand. The older occupants have craniofacial dimensions that demonstrate similarities with mid-Holocene occupants of the southern Sahara and Late Pleistocene to early Holocene inhabitants of the Maghreb. Theirhyperflexed burials compose the earliest cemetery in the Sahara dating to ,7500 B.C.E. These early occupants abandon thearea under arid conditions and, when humid conditions return ,4600 B.C.E., are replaced by a more gracile people withelaborated grave goods including animal bone and ivory ornaments.Conclusions/Significance: The principal significance of Gobero lies in its extraordinary human, faunal, and archaeologicalrecord, from which we conclude the following:(1) The early Holocene occupants at Gobero (7700–6200 B.C.E.) were largely sedentary hunter-fisher-gatherers withlakeside funerary sites that include the earliest recorded cemetery in the Sahara.(2) Principal components analysis of craniometric variables closely allies the early Holocene occupants at Gobero with askeletally robust, trans-Saharan assemblage of Late Pleistocene to mid-Holocene human populations from the Maghreband southern Sahara.(3) Gobero was abandoned during a period of severe aridification possibly as long as one millennium (6200–5200 B.C.E).(4) More gracile humans arrived in the mid-Holocene (5200–2500 B.C.E.) employing a diversified subsistence economybased on clams, fish, and savanna vertebrates as well as some cattle husbandry.(5) Population replacement after a harsh arid hiatus is the most likely explanation for the occupational sequence at Gobero.(6) We are just beginnin