Improved Online Algorithm for Weighted Flow Time

We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(\log P)$-competitive algorithm, where $P$ is the maximum-to-minimum processing time ratio, improving upon the $O(\log^{2}P)$-competitive algorithm of Chekuri, Khanna and Zhu (STOC 2001). We also design a $O(\log D)$-competitive algorithm, where $D$ is the maximum-to-minimum density ratio of jobs. Finally, we show how to combine these results with the result of Bansal and Dhamdhere (SODA 2003) to achieve a $O(\log(\min(P,D,W)))$-competitive algorithm (where $W$ is the maximum-to-minimum weight ratio), without knowing $P,D,W$ in advance. As shown by Bansal and Chan (SODA 2009), no constant-competitive algorithm is achievable for this problem.Comment: 20 pages, 4 figure

Retracted: Inhibition of Corneal Neovascularization by Hydrazinocurcumin

This article previously published in Volume 15 Issue 2 of this journal in February 2016 has been retracted in line with the guidelines from the Committee on Publication Ethics (COPE, http://publicationethics.org/resources/guidelines)Retracted: Zhan W, Zhu J, Zhang Y. Inhibition of corneal neovascularization by hydrazinecurcumin. Trop J Pharm Res 2016; 15(2):349-354 doi: http://dx.doi.org/10.4314/tjpr.v15i2.18

Vertex Algebras W(p)Am\mathcal{W}(p)^{A_m} and W(p)Dm\mathcal{W}(p)^{D_m} and Constant Term Identities

We consider $AD$-type orbifolds of the triplet vertex algebras $\mathcal{W}(p)$ extending the well-known $c=1$ orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras $A(\mathcal{W}(p)^{A_m})$ and $A(\mathcal{W}(p)^{D_m})$, where $A_m$ and $D_m$ are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible $\mathcal{W}(p)^\Gamma$-modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of $m$ and $p$ with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun. Contemp. Math. 15 (2013), 1350028, 30 pages, arXiv:1212.5453; Internat. J. Math. 25 (2014), 1450001, 34 pages, arXiv:1304.5711] provide a complete list of irreducible $\mathcal{W}(p)^{A_m}$ and $\mathcal{W}(p)^{D_m}$-modules. This paper is a continuation of our previous work on the $ADE$ subalgebras of the triplet vertex algebra $\mathcal{W}(p)$

Model development and simulating of a spinning cone evaporator : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology at Institute of Technology and Engineering, Massey University, Palmerston North, New Zealand

The idea of milk pre-concentration at the farm has attracted worldwide interest for many years. A new pilot-scale evaporator (called spinning cone evaporator), which can be operated on the farm and has a compact and efficient design, has been developed at Massey University. However, there is a shortage of knowledge on the design, operation and control of this new evaporator. The main goal of this thesis is to develop a dynamic mathematical model in order to better utilize this evaporator and make further developments. This thesis consists of three parts. Firstly, a first-principles model of a pilot scale spinning cone evaporator is developed using the sub-system modelling techniques of the evaporator from the Laws of Thermodynamics and the general mass and energy balances. The model is dynamic and includes the evaporator, the compressor, the condenser and the product transport sections. The system model describes the dynamic relationships between the input variables (cooling water flowrate, M c , speed of compressor, N comp , feed flowrate, M f , feed temperature, T f and mass composition of feed dry matter, W f ) and the output variables (outlet temperature of cooling water, T co , evaporating temperature, T e , mass composition of product dry matter, w p and product flowrate, M p ), Secondly, the evaporator model was implemented using the software package Matlab along with its dynamic simulation environment Simulink. The differential equations for the evaporator model are embedded in a block diagram representation of the evaporator system. The evaporator Simulink model is divided into three levels, the blocks at the top represent the overall model and global constants used in it. The second level contains the individual sub-systems and the bottom level elements within each sub-system. Results of the model verification are satisfactory. Finally, the model validation is presented for both steady state and dynamic comparisons. The product flowrate (except in the case of feed temperature changes) and evaporation temperature can be predicted at a given time, and the outlet temperature of cooling water and product dry matter composition can also be predicted at a steady state. It can be seen that the results predicted using this spinning cone evaporator model, which accounts for the varying concentrate flowrate and evaporation temperature with time, are in good agreement with experimental data. This model provides a valuable tool to predict performance in a spinning cone evaporator and to modify the design parameters

Actinidin treatment and sous vide cooking : effects on tenderness and in vitro protein digestibility of beef brisket : a thesis presented in partial fulfilment of the requirements for the degree of Master of Food Technology at Massey University, Manawatū, New Zealand

Actinidin from kiwifruit can tenderise meat and help to add value to low-value meat cuts. Compared with other traditional tenderisers (e.g. papain and bromelain) it is a promising way, due to its less intensive tenderisation effects on meat. But, as with other plant proteases, over-tenderisation of meat may occur if the reaction is not controlled. Therefore, the objectives of this study were (1) finding a suitable process to control the enzyme activity after desired meat tenderisation has been achieved; (2) optimising the dual processing conditions- actinidin pre-treatment followed by sous vide cooking to achieve the desired tenderisation in shorter processing times. The first part of the study focused on the thermal inactivation of actinidin in freshly-prepared kiwifruit extract (KE) or a commercially available green kiwifruit enzyme extract (CEE). The second part evaluated the effects of actinidin pre-treatment on texture and in vitro protein digestibility of sous vide cooked beef brisket steaks. The results showed that actinidin in KE and CEE was inactivated at moderate temperatures (60 and 65 °C) in less than 5 min. However, the enzyme inactivation times increased considerably (up to 24 h at these temperatures) for KE/CEE-meat mixtures, compared with KE/CEE alone. The thermal inactivation kinetics were used as a guide for optimising actinidin application parameters during the second phase of the study. For the final experiments, beef steaks were injected with 5 % (w/w, extract/meat) of CEE solution (3 mg/mL) followed by vacuum tumbling (at 4 °C for 15 min) and cooking (at 70 °C for 30 min) under sous vide conditions. This cooking time was considerably less than usual sous vide cooking times used in the meat industry. The actinidin-treated meat had no change in pH and colour, but showed a lower instrumental shear force; and improved sensory scores for tenderness, juiciness and flavour than the untreated meat steaks when tested by a sensory panel. Improved tenderness agreed well with the Transmission Electron Microscopy (TEM) results that showed considerable breakdown of the myofibrillar structure, particularly around the Z line. The addition of actinidin enhanced the rate of breakdown of muscle proteins, as shown by Tricine-sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE), and led to an increase in both protein solubility and ninhydrin-reactive free amino N release, during simulated gastric digestion. These results demonstrate the positive effects of actinidin on meat tenderness and meat protein digestibility during gastric digestion in vitro