A critical fractional equation with concave-convex power nonlinearities

none4sìIn this work we study a fractional critical problem with concave-convex nonlinearities. Our main results show the existence and multiplicity of solutions to this problem for different values of the real parameter appearing in the equation. The dependency on this parameter changes according to whether we consider the concave power case or the convex power case. These two cases will be treated separatelyopenBarrios B; Colorado E; Servadei R; Soria FBarrios, B; Colorado, E; Servadei, Raffaella; Soria, F

On some Critical Problems for the Fractional Laplacian Operator

We study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional Laplacian: (-\Delta)^{\alpha/2}u=\lambda u^q+u^{\frac{N+\alpha}{N-\alpha}}, \quad u>0 &\quad in \Omega, u=0&\quad on \partial\Omega,$$ where $\Omega\subset\mathbb{R}^N$ is a smooth bounded domain, $N\ge1$, $\lambda>0$, $0<q<\frac{N+\alpha}{N-\alpha}$, $0<\alpha<\min\{N,2\}$. For suitable conditions on $\alpha$ depending on $q$, we prove: In the case $q<1$, there exist at least two solutions for every $0<\lambda<\Lambda$ and some $\Lambda>0$, at least one if $\lambda=\Lambda$, no solution if $\lambda>\Lambda$. For $q=1$ we show existence of at least one solution for $01$ the existence is shown for every $\lambda>0$. Also we prove that the solutions are bounded and regular

Caracterización citológica de la médula ósea durante el desarrollo fetal en la alpaca (Vicugna pacos)

The present study aimed to investigate the morphology and morphometry of progenitor cells from the bone marrow through cytological examination during foetal development of the alpaca (Vicugna pacos). Bone marrow samples were collected from 18 culled and clinically healthy alpaca foetuses in Pasco, Peru. The eighth and ninth ribs were removed using the cost-chondral junction as reference and smears were made with the bone marrow samples, and then stained with Wright. The percentages of cellularity for each third of pregnancy were 16 ± 0.2 (n= 3), 35 ± 0.16 (n= 5) and 78 ± 0.12 (n=10), respectively, showing the first hematopoietic cells from 201.5 days old. Through the differential count of 500 cells, the myeloid: erythroid ratio was established, being 0.47 ± 0.27 and 0.69 ± 0.19 for the first, second and last third of pregnancy, respectively. In the second third of pregnancy 10.17% of erythroid cells, 5.03% of myeloid cells and 84.80% of other cell types were detected, while in the last third it was 39.99% of erythroid cells, 26.99% of myeloid cells and 33.21% of other cell types. In the morphometric examination, hematopoietic cells revealed characteristics like those found in other species.El presente estudio tuvo como objetivo investigar la morfología y morfometría de las células progenitoras de la médula ósea a través del examen citológico durante el desarrollo fetal de la alpaca (Vicugna pacos). Se colectaron muestras de médula ósea provenientes de 18 fetos de alpacas clínicamente sanas y destinadas a beneficio en Pasco, Perú. Se seccionaron la octava y novena costillas tomando como referencia la unión costo-condral y se hicieron frotis con las muestras de médula ósea, que fueron coloreadas con la tinción Wright. Los porcentajes de celularidad para cada tercio de gestación fueron 16 ± 0.2 (n=3), 35 ± 0.16 (n=5) y 78 ± 0.12 (n=10), respectivamente, evidenciándose las primeras células hematopoyéticas a partir de los 201.5 días de edad. Mediante el conteo diferencial de 500 células se estableció la relación mieloide:eritroide, siendo de 0, 0.47 ± 0.27 y 0.69 ± 0.19 para el primer, segundo y tercer tercio de gestación, respectivamente. En el segundo tercio de gestación se detectó 10.17% de células eritroides, 5.03% de células mieloides y 84.80% de otros tipos celulares, mientras que en el último tercio fue de 39.99% de células eritroides, 26.99% de células mieloides y 33.21% de otros tipos celulares. En el examen morfométrico, las células hematopoyéticas revelaron características similares a las encontradas en otras especies

Circulating myostatin is reduced with aging in humans but not altered by short-term, high intensity training

Introduction: Ageing involves a loss of muscle mass and function. The rate of decline is associated with negative health outcomes and increased mortality (1). Muscle atrophy is observed at a predictable rate from 30 years of age (2), however maintenance of function is seen in masters athletes > 60 years of age (3). Myostatin acts as a negative regulator of muscle mass (4) and underlies hypertrophy with chronic resistance training (5) and atrophy in chronic conditions (4). Experiment 1: Declared healthy participants (n = 83, 18 - 75 years of age, 36 male, 47 female) were recruited. Body composition, metabolic rate, grip strength and 6-minute walk test were recorded. Venous blood was collected and total myostatin concentration (herein referred to as myostatin) quantified by enzyme-linked immunosorbent assay. Total myostatin was lower in females compared with males (2176.1 [135.3] vs. 2788.7 [180.2] pg.mL-1 [p = 0.007]). Stepwise regression observed that myostatin concentration is best predicted firstly by gender, then by age (r = 0.399, p = 0.02), and was not further improved by the addition of measures of metabolism, muscle mass or function. Experimental 2: A cohort of aged sedentary (SED) males (n = 14; 63.9 [5.6] years of age) and masters athletes (lifelong exerciser [LEX]; n = 10, 61.1 [5.8] years of age) completed 6 weeks of high intensity interview training (HITT). Two way ANOVA suggested no group (SED, LEX) × time (pre, post) interaction on myostatin concentration (p = 0.649), nor a main effect of time (p = 0.757), however there was a trend towards increased myostatin in the LEX group relative to SED (p = 0.083). Discussion: Loss of muscle mass and function occurs at a predictable rate from ~30 years of age, however the rate of loss differs between active and inactive populations. Here we demonstrate that total circulating myostatin decreases as age increases, and differs significantly between males and females. Total circulating myostatin negatively correlates with increasing age, however alterations in myostatin do not appear after short term training interventions. Longer term activity may alter myostatin, thus our next work will follow up experiment 2 with a 3 year longitudinal analysis

Yield gaps, nutrient use efficiencies and response to fertilisers by maize across heterogeneous smallholder farms of western Kenya

The need to promote fertiliser use by African smallholder farmers to counteract the current decline in per capita food production is widely recognised. But soil heterogeneity results in variable responses of crops to fertilisers within single farms. We used existing databases on maize production under farmer (F-M) and researcher management (R-M) to analyse the effect of soil heterogeneity on the different components of nutrient use efficiency by maize growing on smallholder farms in western Kenya: nutrient availability, capture and conversion efficiencies and crop biomass partitioning. Subsequently, we used the simple model QUEFTS to calculate nutrient recovery efficiencies from the R-M plots and to calculate attainable yields with and without fertilisers based on measured soil properties across heterogeneous farms. The yield gap of maize between F-M and R-M varied from 0.5 to 3 t grain ha-1 season-1 across field types and localities. Poor fields under R-M yielded better than F-M, even without fertilisers. Such differences, of up to 1.1 t ha-1 greater yields under R-M conditions are attributable to improved agronomic management and germplasm. The relative response of maize to N-P-K fertilisers tended to decrease with increasing soil quality (soil C and extractable P), from a maximum of 4.4-fold to -0.5- fold relative to the control. Soil heterogeneity affected resource use efficiencies mainly through effects on the efficiency of resource capture. Apparent recovery efficiencies varied between 0 and 70% for N, 0 and 15% for P, and 0 to 52% for K. Resource conversion efficiencies were less variable across fields and localities, with average values of 97 kg DM kg-1 N, 558 kg DM kg-1 P and 111 kg DM kg-1 K taken up. Using measured soil chemical properties QUEFTS over-estimated observed yields under F-M, indicating that variable crop performance within and across farms cannot be ascribed solely to soil nutrient availability. For the R-M plots QUEFTS predicted positive crop responses to application of 30 kg P ha-1 and 30 kg P ha-1 + 90 kg N ha-1 for a wide range of soil qualities, indicating that there is room to improve current crop productivity through fertiliser use. To ensure their efficient use in sub-Saharan Africa mineral fertilisers should be: (1) targeted to specific niches of soil fertility within heterogeneous farms; and (2) go hand-in-hand with the implementation of agronomic measures to improve their capture and utilisation