A characterization of quadric constant mean curvature hypersurfaces of spheres

Let $\phi:M\to\mathbb{S}^{n+1}\subset\mathbb{R}^{n+2}$ be an immersion of a complete $n$-dimensional oriented manifold. For any $v\in\mathbb{R}^{n+2}$, let us denote by $\ell_v:M\to\mathbb{R}$ the function given by $\ell_v(x)=\phi(x),v$ and by $f_v:M\to\mathbb{R}$, the function given by $f_v(x)=\nu(x),v$, where $\nu:M\to\mathbb{S}^{n}$ is a Gauss map. We will prove that if $M$ has constant mean curvature, and, for some $v\ne{\bf 0}$ and some real number $\lambda$, we have that $\ell_v=\lambda f_v$, then, $\phi(M)$ is either a totally umbilical sphere or a Clifford hypersurface. As an application, we will use this result to prove that the weak stability index of any compact constant mean curvature hypersurface $M^n$ in $\mathbb{S}^{n+1}$ which is neither totally umbilical nor a Clifford hypersurface and has constant scalar curvature is greater than or equal to $2n+4$.Comment: Final version (February 2008). To appear in the Journal of Geometric Analysi

SOCIO-DEMOGRAPHIC AND PSYCHOLOGICAL DETERMINANTS OF LEISURE TIME PHYSICAL ACTIVITY AMONG ADOLESCENTS IN NIGERIA

Despite the numerous benefits associated with leisure time physical activity (LTPA), it is quite worrisome that the habit of regularly engaging in LTPA is rare among Nigerians, especially among adolescents who are found in myriads of sedentary lifestyle behaviour as a result of technological and economical advancement. The present study examined socio-demographic and psychological determinants of LTPA among adolescents in Nigeria. A cross-sectional study was conducted and multistage sampling technique was employed to recruit 1200 adolescents (Male =59.7%; Female =40.3%; Age: 10-19years) from twelve secondary schools in Southwest States, Nigeria. Physical Activity Self-Efficacy for Adolescent (PASE), The Physical Activity and Leisure Motivation Scale (PALMS), Activity Questionnaire for Adults and Adolescents (AQuAA) and Self-developed Socio-demographic Questionnaire were used to collect the data. Data were analyzed using statistics of frequency count, percentages & Multiple Regression. The result of the study showed that socio-demographic (F(8,1191) = 4.980; p< .05; R2 = .28) accounting for 28% of its variance and psychological factors (F (2,1197) =31014.342, p< .05; R2 = .99) accounting for 99% of its variance) were significant. Based on the findings, adolescents in Southwest states in Nigeria do not meet the World Health Organization recommendations on physical activity. Both socio-demographic and psychological factors significantly determined LTPA and these factors could be taken into account in the development of interventions to increase LTPA levels throughout the life course among adolescents in Nigeria.   Article visualizations

Offshore Topside Rotating Packed Bed as Process Intensified Alternative for Natural Gas Sweetening and Dehydration

This work is aimed at investigating the benefits of replacing conventional process unit operations with process intensified ones in offshore applications. This ensures that better use is made of raw materials, lower energy consumption and a reduced plant volume was achieved. Specifically, a rotating packed bed technology has been used for gas dehydration and sweetening. To achieve the aim of this study, a process intensification approach is used to redesign mature absorption processes to more compact and efficient one. Process simulation using Aspen Hysys was carried out for Triethylene glycol dehydration and monoethanolamine sweetening. More than 36-fold absorption unit size reduction was achieved thereby effecting large decrease in capital and operating costs compared to the conventional packed columns currently utilized in the offshore oil and gas industry. The process intensified technologies therefore can be deployed for offshore applications where space and size considerations are of utmost importance

Radiological assessment of natural radionuclide contents in soils from Omala, Kogi State, Nigeria.

High purity germanium detector (HPGe) was employed to assess radionuclide contents of 238U, 40K and 232Th in soils obtained from Omala, Kogi State, Nigeria. The activities measured vary from 9.0 to 82.2, 12.3 to 114.86 and below detector limit (BDL) and 349.0 Bq Kg-1 in 238U, 232Th and 40K respectively. Highest activities for the three radionuclides were consistently obtained from soil samples got from Igaliwu. The measured activities were engaged to estimate the absorbed dose, annual outdoor effective dose and gamma index. It was observed from the absorbed dose, annual equivalent dose and the gamma index estimated that soils from Igaliwu, Ijeke-ogene and Bagana were found to be higher than the recommended safe limit for normal background. This suggests that those living or using the soil for construction purposes are exposed to high radiation burden from natural radionuclides

Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements

A generic model of stochastic autocatalytic dynamics with many degrees of freedom $w_i$ $i=1,...,N$ is studied using computer simulations. The time evolution of the $w_i$'s combines a random multiplicative dynamics $w_i(t+1) = \lambda w_i(t)$ at the individual level with a global coupling through a constraint which does not allow the $w_i$'s to fall below a lower cutoff given by $c \cdot \bar w$, where $\bar w$ is their momentary average and $0<c<1$ is a constant. The dynamic variables $w_i$ are found to exhibit a power-law distribution of the form $p(w) \sim w^{-1-\alpha}$. The exponent $\alpha (c,N)$ is quite insensitive to the distribution $\Pi(\lambda)$ of the random factor $\lambda$, but it is non-universal, and increases monotonically as a function of $c$. The "thermodynamic" limit, N goes to infty and the limit of decoupled free multiplicative random walks c goes to 0, do not commute: $\alpha(0,N) = 0$ for any finite $N$ while $\alpha(c,\infty) \ge 1$ (which is the common range in empirical systems) for any positive $c$. The time evolution of ${\bar w (t)}$ exhibits intermittent fluctuations parametrized by a (truncated) L\'evy-stable distribution $L_{\alpha}(r)$ with the same index $\alpha$. This non-trivial relation between the distribution of the $w_i$'s at a given time and the temporal fluctuations of their average is examined and its relevance to empirical systems is discussed.Comment: 7 pages, 4 figure

Dealing with uncertainty in GHG inventories: How to go about it?

The assessment of greenhouse gases emitted to and removed from the atmosphere is high on both political and scientific agendas. Under the United Nations Framework Convention on Climate Change, Parties to the Convention publish annual or periodic national inventories of greenhouse gas emissions and removals. Policymakers use these inventories to develop strategies and policies for emission reductions and to track the progress of these policies. However, greenhouse gas inventories (whether at the global, national, corporate, or other level) contain uncertainty for a variety of reasons, and these uncertainties have important scientific and policy implications. For scientific, political, and economic reasons it is important to deal with the uncertainty of emissions estimates proactively. Proper treatment of uncertainty affects everything from our understanding of the physical system to the economics of mitigation strategies and the politics of mitigation agreements. A comprehensive and consistent understanding of, and a framework for dealing with, the uncertainty of emissions estimates should have a large impact on the functioning and effectiveness of the Kyoto Protocol and its successor. This chapter attempts to pull together relevant fragments of knowledge, allowing us to get a better picture of how to go about dealing with the uncertainty in greenhouse gas inventories

Constraints on relaxation rates for N-level quantum systems

We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open N-level systems. The Lindblad operators that govern the evolution of the system are expressed in terms of observable relaxation rates, explicit formulas for the decoherence rates due to population relaxation are derived, and it is shown that there are additional, non-trivial constraints on the pure dephasing rates for N>2. Explicit experimentally testable inequality constraints for the decoherence rates are derived for three and four-level systems, and the implications of the results are discussed for generic ladder-, Lambda- and V-systems, and transitions between degenerate energy levels.Comment: 10 pages, RevTeX, 4 figures (eps/pdf

Gas Chromatography Mass Spectrometry Identification of Antiangiogenic Phytochemicals in Aframomum danielli K. Schum: An In silico Study

Aframomum danielli is one of the African spices used in folklore medicine for the management of several diseases. This study identified the phytochemical components present in the n-hexane seed extract of the A. danielli by gas chromatography-mass spectrometry (GC-MS) analysis and also evaluated the antiangiogenic potential of the identified phytochemicals by performing molecular docking against human Vascular Endothelial Growth Factor (VEGF) and matrix metalloproteinases (MMP) using Molegro Virtual Docker. The GC-MS analysis identified the presence of phytochemical components β-Caryophyllene (RT: 18.479), α-Caryophyllene (RT: 19.189), (4-Hydroxy-3-methoxyphenyl)ethyl methyl ketone (RT: 22.976), N-Acetyl-m-aminobenzoic acid (RT: 31.651) and 3-Pyridineacetic acid (RT: 32.446). (4-Hydroxy- 3-methoxyphenyl)ethyl methyl ketone were the strongest binding ligand (-65.744 kcal/mol for VEGF) and (- 99.7836kcal/mol for MMP) while β-Caryophyllene was the weakest binding ligand. These compounds showed relative strong docking to VEGF with docking energies comparable to an anticancer drug, bevacizumab (-77.883kcal/mol for VEGF) and (-109.021kcal/mol for MMP). This in silico molecular docking study has shown that these phytochemical components could be responsible for antiangiogenic properties of A. danielli

Minimal cubic cones via Clifford algebras

We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any $n\ge4$, $n\ne 16k+1$, there is at least one minimal cone in $R^{n}$ given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in $R^{m^2}$, $m\ge2$, defined by an irreducible homogeneous polynomial of degree $m$. These examples provide particular answers to the questions on algebraic minimal cones posed by Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table