A note on new weighted geometric inequalities for hypersurfaces in Rn\mathbb R^n

In this note, we prove a family of sharp weighed inequality which involves weighted $k$-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in $\mathbb{R}^n$. This inequality generalizes the corresponding result of Wei and Zhou \cite{WZ} where their proof is based on earlier results of Kwong-Miao \cite{KM1,KM2}. Here we present a proof which does not rely on Kwong-Miao's results.Comment: 7 page

MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE

Let K-1, K-2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a is an element of K-1, b is an element of K-2}. We show that the set K1K2 is star-haped if K-1 is a line segment or a circular disk. Examples for K-1 and K-2 are given so that K-1 and K-2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science. Additional results and open problems are presented

Phase equilibria of polydisperse hydrocarbons: moment free energy method analysis

We analyze the phase equilibria of systems of polydisperse hydrocarbons by means of the recently introduced moment method. Hydrocarbons are modelled with the Soave-Redlick-Kwong and Peng-Robinson equations of states. Numerical results show no particular qualitative difference between the two equations of states. Furthermore, in general the moment method proves to be an excellent method for solving phase equilibria of polydisperse systems, showing excellent agreement with previous results and allowing a great improvement in generality of the numerical scheme and speed of computation.Comment: 12 pages, 2 figure

Knowledge super corridors in Southeast Asia: seeing and doing from a critical lens

Developing countries in Asia are in the process of transitioning from a production economy to a knowledge-based economy. Various new knowledge and information communications technology mega-projects are being designed and executed at the international, national, state and industry levels to sustain competitiveness. The structures and processes by which these so-called “knowledge super corridors” are developed and implemented are complex economic-social-political decisions. The author develops an enhanced framework from critical theory, whereby the critical practice lens provides an iterative reflexive process, firstly by developing knowledge for understanding from structuration theory. Secondly, the author provides a critique of underpinning assumptions and presumptions whereby the constraining conditions of the status quo and emancipation become knowable and explicit, that is, knowledge for evaluation. Thirdly, the knowledge for action generated will enable the decision makers to re-create, re-define, re-design, re-imagine, re-invent and re-vision pragmatic, doable and implementable programs to transform a developing country into a k-economy. The author illustrates the value of the enhanced model using two case studies concerned with formulating and implementing a k-economy blueprint and developing a knowledge portal in emerging k-economies in Southeast Asia

Generalized pairwise z-complementary codes

An approach to generate generalized pairwise Z-complementary (GPZ) codes, which works in pairs in order to offer a zero correlation zone (ZCZ) in the vicinity of zero phase shift and fit extremely well in power efficient quadrature carrier modems, is introduced in this letter. Each GPZ code has MK sequences, each of length 4NK, whereMis the number of Z-complementary mates, K is a factor to perform Walsh–Hadamard expansions, and N is the sequence length of the Z-complementary code. The proposed GPZ codes include the generalized pairwise complementary (GPC)codes as special cases

A Hardy-Littlewood Integral Inequality on Finite Intervals with a Concave Weight

A Hardy-Littlewood integral inequality on finite intervals with a concave weight is established. Given a function f on an interval [a,b], it is shown that the square of the weighted L^2 norm of its derivative f' is bounded by the product of the weighted L^2 norm of f and that of the second derivative f''.Comment: To appear in: Periodica Mathematica Hungaric

Wireless sensor network for cattle monitoring system

This paper describes a cost effective Wireless Sensor Network (WSN) technology for monitoring the health of dairy cows. By monitoring and understanding the cow individual and herd behaviour, farmers can potentially identify the onset of illness, lameness or other undesirable health conditions. However, the WSN implementation needs to cope with various technical challenges before it can be suitably and routinely applied in cow management. This paper discusses results concerning data transportation (i.e. mobility) from the cow mounted sensory devices