Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Strength properties of polymer mortar panels using methyl methacrylate solution of waste expanded polystyrene as binder

The present study examines the applicability of polymermortarpanels using a methylmethacrylate (MMA) solution of wasteexpandedpolystyrene (EPS) to develop effective recycling processes for the EPS, referring to the strengthproperties of a polymer-impregnated mortarpanel with almost the same performance as commercial products. An MMA solution of EPS is prepared by dissolving EPS in MMA, and unreinforced and steel fiber-reinforced polymermortars are mixed using the EPS-MMA-based solution as a liquid resin or binder. Polymermortarpanels (PMPs) using the EPS-MMA-based polymermortars without and with steel fiber and crimped wire cloth reinforcements and steel fiber-reinforced polymer-impregnated mortarpanel (PIMP) are prepared on trial, and tested for flexural behavior under four-point loading. The EPS-MMA-based PMPs are more ductile than the PIMP, and have a high load-bearing capacity. Consequently, they can replace PIMP in practical applications

Small volume expansions for elliptic equations

This paper analyzes the influence of general, small volume, inclusions on the trace at the domain's boundary of the solution to elliptic equations of the form \nabla \cdot D^\eps \nabla u^\eps=0 or (-\Delta + q^\eps) u^\eps=0 with prescribed Neumann conditions. The theory is well-known when the constitutive parameters in the elliptic equation assume the values of different and smooth functions in the background and inside the inclusions. We generalize the results to the case of arbitrary, and thus possibly rapid, fluctuations of the parameters inside the inclusion and obtain expansions of the trace of the solution at the domain's boundary up to an order \eps^{2d}, where $d$ is dimension and \eps is the diameter of the inclusion. We construct inclusions whose leading influence is of order at most \eps^{d+1} rather than the expected \eps^d. We also compare the expansions for the diffusion and Helmholtz equation and their relationship via the classical Liouville change of variables.Comment: 42 page

Mechanical and durability performance of lightweight concrete brick with palm oil fuel ash (POFA)

Lightweight building materials such as precast roof and wall panel has been widely used in the construction industries. This is because lightweight materials could benefits the economy and society in terms of manufacturing, transportation and handling cost. One of the most preferable lightweight material is Expanded Polystyrene (EPS). EPS consist of 98% of air and 2% of polystyrene. Therefore, EPS is very low in density which could contribute in the reduction of building materials mass. Abundance of studies has shown that EPS has significantly contribute to the reduction of brick density. EPS has been used as the aggregates replacement in concrete. However, the existing of EPS in the concrete has reduce the strength performance of the concrete. Due to this, researchers have extend their research in improvising the EPS concrete and brick strength with the addition of pozzolanic materials such as fly ash, rice husk ask, silica fume and etc [1-4]. The ability of these pozzolanic materials in enhancing the strength of brick or concrete has been proven..

Distributed Maximum Matching in Bounded Degree Graphs

We present deterministic distributed algorithms for computing approximate maximum cardinality matchings and approximate maximum weight matchings. Our algorithm for the unweighted case computes a matching whose size is at least (1-\eps) times the optimal in \Delta^{O(1/\eps)} + O\left(\frac{1}{\eps^2}\right) \cdot\log^*(n) rounds where $n$ is the number of vertices in the graph and $\Delta$ is the maximum degree. Our algorithm for the edge-weighted case computes a matching whose weight is at least (1-\eps) times the optimal in \log(\min\{1/\wmin,n/\eps\})^{O(1/\eps)}\cdot(\Delta^{O(1/\eps)}+\log^*(n)) rounds for edge-weights in [\wmin,1]. The best previous algorithms for both the unweighted case and the weighted case are by Lotker, Patt-Shamir, and Pettie~(SPAA 2008). For the unweighted case they give a randomized (1-\eps)-approximation algorithm that runs in O((\log(n)) /\eps^3) rounds. For the weighted case they give a randomized (1/2-\eps)-approximation algorithm that runs in O(\log(\eps^{-1}) \cdot \log(n)) rounds. Hence, our results improve on the previous ones when the parameters $\Delta$, \eps and \wmin are constants (where we reduce the number of runs from $O(\log(n))$ to $O(\log^*(n))$), and more generally when $\Delta$, 1/\eps and 1/\wmin are sufficiently slowly increasing functions of $n$. Moreover, our algorithms are deterministic rather than randomized.Comment: arXiv admin note: substantial text overlap with arXiv:1402.379

Incorporation of extracellular polysaccharide produced by Xanthomonas campestris into milk powders : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology in Food Technology at Massey University

The purpose of the research was to investigate the functional properties of milk powders following exopolysaccharide (EPS) addition to milk solutions and their subsequent spray-drying. The aim was to replace some of the milk proteins with polysaccharide in dairy products while maintaining or improving the functional characteristics. Both commercial xanthan EPS and ferment xanthan EPS were incorporated into whole milk powder (WMP), skim milk powder (SMP), and milk protein concentrate (MPC). Ferment EPS was produced from a by-product of the dairy industry, milk permeate, through the hydrolysis of the lactose and fermentation with a strain of Xanthomonas campestris. Ferment EPS had a characteristic and unpleasant odour. The main compound responsible for this odour was p-cresol which, in milk, is largely bound in the conjugate form. Xanthomonas campestris hydrolyses these conjugates releasing the odour compounds. Ultrafiltration (UF) of the ferment or passing the ferment through a bed of activated carbon was effective in reducing the odour. UF was proven to reduce the levels of p-cresol in the ferment from 138ppb to less than 5ppb after 98 concentration factors. Milk powders made with UF ferment were more acceptable to the consumer sensory panel than those made with untreated ferment. The incorporation of EPS into milk powders has beneficial effects on the product with small additions increasing the viscosity of reconstituted SMP and WMP considerably. The EPS addition could result in a thickened milk product or alternatively, substitute for some of the milk solids. Sensory testing showed that 13.3% WMP solution, containing 0.02% commercial EPS, was not detectably different from a 15% WMP solution. The addition of both commercial and ferment EPS into milk powders leads to the formation of separate flocculated casein and polysaccharide phases with reconstituted milk. Confocal microscopy showed that casein flocculation occurred at all EPS concentrations tested, but this only resulted in sedimentation at intermediate EPS concentrations. At high EPS concentrations of approximately 0.2% the high viscosity limited flocculation and prevented sedimentation. At low EPS concentrations of approximately 0.05% flocculation was insufficient to overcome Brownian motion. Fresh cheese (Panela) made from MPC containing either ferment or commercial EPS showed greatly decreased whey loss. This was attributed to (i) the increased viscosity of the continuous phase limiting the flow of liquid through the pores of the cheese, and (ii) diminished casein interaction in the presence of EPS leading to a looser curd and lower contraction forces. For example the incorporation of 0.161% ferment EPS decreased the whey lost by approximately 75%. Negative effects were also apparent. The addition of EPS led to a granular appearance, which became more apparent with increasing EPS concentration. Cheese firmness was also decreased by approximately 40% by the addition of the ferment EPS at 0.161%. This could also be attributed to the localised aggregation of protein during renneting and the increased heterogeneity of the network. Sensory testing of cheeses made with 15.6% MPC + 0.045% commercial EPS compared with cheese made with 17.37% MPC alone showed that the consumers had no significant preference for one cheese over the other, but did notice a difference in texture. For reasons of safety and health, the sensory testing of milk and cheese in this research was confined to commercial xanthan. Future sensory testing of milk and cheese should be conducted with ferment EPS after odour removal rather than commercial EPS, and use consumers familiar with these cheese and milk products. For commercial production of dairy powders containing UF ferment EPS it is vital that either the xanthan or casein micelle structure be altered to prevent casein flocculation. If this is not feasible then an alternative use of the product may need to be found. A potential option involves the addition of the powder containing UF ferment EPS into food products as a minor food constituent. This may limit the occurrence of phase separation while improving the functionality of the product. Commercialisation is also limited by the increasing costs caused by ferment EPS purification and the lower solids concentrations required for spray-drying. As such the viability of the powder production must be determined