Quadratic Mathematical Model Research Articles

Modeling antimicrobial activity of lipopeptides from Bacillus amyloliquefaciens ES-2 against Shewanella putrefaciens in shrimp meat using a response surface method.

Bacillus amyloliquefaciens ES-2 can produce antimicrobial lipopeptides, including surfactin and fengycin. In this study, the model of antimicrobial activity against Shewanella putrefaciens in shrimp meat by antimicrobial lipopeptides from B. amyloliquefaciens ES-2 was researched by response surface methodology. The results showed that S. putrefaciens had high sensitivity to antimicrobial lipopeptides, which had a MIC of 0.6 mg/ml. A quadratic mathematical model representative of the action of antimicrobial lipopeptides on S. putrefaciens in shrimp meat was developed as a function of concentration, time, and temperature. A reduction of S. putrefaciens cells of over 2 log cycles could be realized when the temperature was below 5.4°C, the time was over 6 h, and the concentration of the lipopeptides was over 0.3 mg/g.

Synthesis of silver nano catalyst by gel-casting using response surface methodology

Ceria supported silver nano catalyst was synthesized using a simple, fast and cost-effective gel‐casting technique. The gel was made of acryl amide monomer (AM) to disperse, stabilize and control the size of metal nanoparticles. The obtained results revealed that nano particles can easily be confined into the three dimensional network of the polymeric gel. The polymer matrix was then removed by calcination under a controlled atmosphere and temperature. A central composite experimental design, which is one of the most popular designs of response surface methodology, was used to optimize the production parameters influencing the surface area and particle size. The studied parameters were the amount of cross-linker (N,N′-methylenebisacrylamide (MBAM)), the monomer (AM) to cross linker ratio and the monomer to salt (silver nitrate) ratio. Two quadratic mathematical model equations were derived for predicting the surface area and particle size. Analysis of the variance showed that the AM/salt ratio was the most significant factor affecting the surface area of nanoparticles. In the process optimization, the maximum amount of surface area was achieved concurrently with the minimum values for particle size at 5.38m2/g and 190nm, respectively. The optimal ranges of the AM/salt ratio and the amount of MBAM to achieve the minimum particle size were 46.97–49.43 and 0.38–0.51, respectively. The optimal values of the MBAM, AM/MBAM and AM/salt ratio for the maximum surface area of 6.09m2/g were found to be 0.54g, 33.92 and 51.89, respectively.

Prediction of MEUF process performance using artificial neural networks and ANFIS approaches

In the present study, a micellar-enhanced ultrafiltration (MEUF) procedure for the separation of lead ions from aqueous solution using response surface methodology (RSM) has been proposed. Due to the extreme complexity and nonlinearity of membrane separation processes, two models, including a feed forward artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS) have been utilized. These simulation methods have been given extreme accurate model that are more efficient than the second quadratic mathematical model for both response variables. The results of ANN and ANFIS models have been shown that the independent predicted rejection and permeate values were compared to measured target values and good correlations were found (R2>0.92, R2>0.97) for two above mentioned approaches, respectively.

Process Optimization of Microwave Drying Sludge with Response Surface Methodology

To enhance further treatment efficiency of the sludge, a process microwave drying of sludge was optimized using response surface methodology (RSM). A quadratic polynomial mathematical model was developed through Box-Behnken experimental design to describe the relationship between tested variables and moisture content of sludge. The experimental values were found to be in accordance with the predicted values, the correlation coefficient is 0.9203(P < 0.001). Estimated optimum parameters were as follows: The sludge: tree bark is 58:1, microwave power is 630w and processing time is 5.32 minutes. Under these conditions, a lowest moisture content of sludge (49.12%) after microwave drying was reached.

Study of Salinity and pH Effects on Gelation Time of a Polymer Gel Using Central Composite Design Method

Experiments were conducted to investigate the main effects of salinity (NaCl) concentrations and pH factors and their interactions on the gelation time response of a polymer gel used in a water shutoff system in oil field reservoirs. Central composite design (CCD) was used to design experiments and a mathematical model building. The main advantage of CCD was to generate the quadratic mathematical model for the gelation time as functions of salinity and pH factors. Tests were limited and optimized by CCD points including low star (axial), low factorial, central, high factorial, and high star points. The evaluation of the data and the developed model were performed through the examination of graphical trend of residuals and a numerical approach. Analysis of variance (ANOVA) was used to estimate the amount of data variations from the model predictions. It was found that the model was significant at the 99% confidence against test data. The results showed that the gelation time was dependent more on pH than salinity. For low pH, the gelation time increased with increasing of the salinity, while for a high pH (>4) the relationship was inversed. The research shows that CCD can effectively be applied for the modeling of gelation time and finding an optimum condition to achieve maximum or minimum gelation time for different salinity and pH factors.

Modeling of sporicidal effect of hydrogen peroxide in the sterilization of low density polyethylene film inoculated with Bacillus subtilis spores

The sporicidal effect of hydrogen peroxide (H2O2) in the sterilization of low density polyethylene film (LDPE) was evaluated using a Central Composite Design (CCD). The effects of contact time (5-19s), bath temperature (23–70 °C) and concentration of H2O2 (0–35%) in an immersion bath were investigated. A 16 cm2 film surface was evenly inoculated with 100 μL of the test microorganism Bacillus subtilis var. globigii ATCC9372 spores. The effective H2O2 sporicidal activity was demonstrated at concentrations from 18 to 35% and in a temperature range from 46 to 70 °C, resulting in 2–7 decimal reductions of B. subtilis spores. A quadratic mathematical model representative of the action of H2O2 on the B. subtilis spores was developed as a function of concentration, time and temperature. Test specimens sanitized with 28% H2O2 at 60 °C for 8 s showed 4 decimal reductions. In the same sterilization procedure, but extending the time to 16 s, this value increased to 7 decimal reductions, demonstrating the efficiency of H2O2 as a function of contact time. The sterilization system tested showed satisfactory performance in the sterilization of LDPE films, being capable of reaching up to 7 decimal reductions of the bacterial spore population.

Modeling, simulation and parametric optimization of wire EDM process using response surface methodology coupled with grey-Taguchi technique

In the present work, quadratic mathematical models have been derived to represent the process behavior of wire electrical discharge machining (WEDM) operation. Experiments have been conducted with six process parameters: discharge current, pulse duration, pulse frequency, wire speed, wire tension and dielectric flow rate; to be varied in three different levels. Data related to the process responses viz. material removal rate (MRR), roughness value of the worked surface (a measure of surface finish, SF) and kerf have been measured for each of the experimental runs; which correspond to randomly chosen different combinations of factor setting. These data have been utilized to fit a quadratic mathematical model (Response Surface Model) for each of the responses, which can be represented as a function of the aforesaid six process parameters. Predicted data have been utilized for identification of the parametric influence in the form of graphical representation for showing influence of the parameters on selected responses. Predicted data given by the models (as per Taguchi’s L27 (3*6) Orthogonal Array (OA) design) have been used in search of an optimal parametric combination to achieve desired yield of the process: maximum MRR, good surface finish (minimum roughness value) and dimensional accuracy of the product. Grey relational analysis has been adopted to convert this multi-objective criterion into an equivalent single objective function; overall grey relational grade, which has been optimized (maximized) by using Taguchi technique. Optimal setting has been verified through confirmatory test; showed good agreement to the predicted value. This indicates utility of the grey-Taguchi technique as multi-objective optimizer in the field of wire EDM. Keywords: Wire EDM; MRR; response surface methodology; Orthogonal Array (OA)

Development of a solid-state fermentation process for production of an alpha amylase with potentially interesting properties

Ca-independency with potential activity and stability at low pH are among the most interesting characteristics of alpha-amylase in starch industry. In this attempt the synergetic effect of low pH on activity of crude Ca-independent alpha-amylase isolated from a native Bacillus sp. KR-8104 in solid-state fermentation (SSF) was studied using wheat bran (WB) as a substrate. The effects of different parameters including moisturizing agents, solid substrate to moisture ratio, particle size, incubation temperature and period, inoculum (v/w) and supplementation with 1% (w/w) different carbon and nitrogen sources on enzyme production were investigated. Maximum enzyme production of 140U/g dry fermented substrate was obtained from wheat bran moistened with tap water at a ratio of 1:1.5 and supplemented with 1% (w/w) NH(4)NO(3) and 1% (w/w) lactose after 48h incubation at 37 degrees C. Even though the production of alpha-amylase was lower at 40 and 45 degrees C, the viable cell count was higher. In addition response surface methodology (RSM) was applied to find optimum conditions of temperature and pH on crude amylase activity. Using central composite design (CCD) a quadratic mathematical model equation was derived for the prediction of enzyme activity. The results showed that the model was in good agreement with experimental results, with R(2)=0.90 (p<0.0001) and the low pH has a synergetic effect on enzyme activity at higher temperature.

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The study focused on the influence of the variables seawater proportion (%) and bicarbonate concentration on Spirulina sp. biomass production, using a Central Composite Rotational Design (CCRD) to evaluate the optimal regions of biomass production (ϕ), adaptation phase (λ), specific growth rate (µ) and generation time (G), using for each treatment the Gompertz mathematical model. The highest values of biomass (ϕ) log N/N0: 0.93 were obtained at 168.8 hours; in a culture medium with pH 8.8±0.1; at a temperature of 25°C; with salinity of 1.2% and 1.6 gL of bicarbonate. The lowest value of ϕ was 0.45±0.01; coincidentally obtained in repetitions of the central point, using a salinity of 0.7% and 3.0g/L of bicarbonate; in a medium with pH 9.1±0.4 to 25°C; which shows the importance of salinity provided by the volume of seawater relative to bicarbonate, in the production of Spirulina biomass. The lighting was 2.7±1.2 klx, provided by a White Light-Emitting Diode (WLED) during 12 continuous hours and an air injection of 0.86±0.09 L/s by a photo bioreactor with a 200 mL capacity. Only the values of ϕ, adjusted properly to the Response Surface with an R2 of 0.99 for a quadratic mathematical model and p < 0.05 with a 2.4% average absolute error.

Precipitation of Germanium from Coal Fly Ash Leachates

The valorization of a coal gasification fly ash was studied by leaching the fly ash using different aqueous solutions followed by the subsequent precipitation of the germanium solubilized from the ash. Experimental investigations were focused on the precipitation of a germanium-catechol (CAT) complex with cetyl trimethyl ammonium bromide (CTAB). The influences of pH and amounts of CTAB and CAT on the precipitation yield were investigated. To this aim, a central composite rotatable design and ANOVA Design Expert 7.0.3 Wiley software were employed for experimental design and analysis of the results. Thus, the independent and combined effects of pH, CAT/Ge and CTAB/Ge molar ratios were investigated and optimized using a quadratic mathematical model. The optimum values of these factors were found to be 10, 12, and 4, respectively (in this case, the germanium precipitation yield was 98.8% for water leachates). The precipitation of germanium as a complex compound with CAT and CTAB was found to be selective towards germanium and this element can be effectively separated from As, Mo, Sb, V, or Zn. Total organic carbon in solution was measured to estimate the amounts of CAT and CTAB precipitated with germanium and with the interferences present in aqueous leachates. In addition, thermogravimetric analyses have been performed on the germanium-complex solids as a result of which 600°C was determined as the minimum temperature to completely remove the organic content of the precipitate.

Thermoreversible mucoadhesive ophthalmic in situ hydrogel: Design and optimization using a combination of polymers

The purpose of the study was to develop an optimized thermoreversible in situ gelling ophthalmic drug delivery system based on Pluronic F 127, containing moxifloxacin hydrochloride as a model drug. A 3(2) full factorial design was employed with two polymers: Pluronic F 68 and Gelrite as independent variables used in combination with Pluronic F 127. Gelation temperature, gel strength, bioadhesion force, viscosity and in vitro drug release after 1 and 10 h were selected as dependent variables. Pluronic F 68 loading with Pluronic F 127 was found to have a significant effect on gelation temperature of the formulation and to be of importance for gel formation at temperatures 33-36 °C. Gelrite loading showed a positive effect on bioadhesion force and gel strength and was also found helpful in controling the release rate of the drug. The quadratic mathematical model developed is applicable to predicting formulations with desired gelation temperature, gel strength, bioadhesion force and drug release properties.

Optimization and evaluation of acetylcholine esterase immobilization on ceramic packing using response surface methodology

In the present attempt a method for the immobilization of acetylcholine esterase (AChE) was developed. In this method, the enzyme was immobilized onto a ceramic cylinder support using a sol–gel–multiwall carbon nanotube (MWCNT) composite. Response surface methodology (RSM) was used for the design and analysis of immobilization experiments. Quadratic mathematical model equations were derived for the prediction of enzyme activity. Then the effects on enzyme activity at 30, 40 and 50 min after process initiation of varying each of two parameters over five levels were investigated. These parameters were the AChE:MWCNT ratio ( X 1), and AChE–MWCNT:sol–gel ratio ( X 2). The optimum values of X 1 and X 2 for the immobilization of AChE on ceramic packing were found to be 1.07 and 0.43, respectively. Using these optimum parameters it was shown that enzyme immobilization with MWCNTs and sol–gel was more effective than immobilization with sol–gel or graphite and sol–gel. Scanning electron microscopic (SEM) images revealed a porous surface comprised of MWCNT–AChE encapsulated in sol–gel. Furthermore, the system was highly reproducible with standard deviations after three successive assays of 1.88%, 2.11% and 2.13% at 30, 40 and 50 min after process initiation, respectively.

Gastric floating matrix tablets: Design and optimization using combination of polymers

The purpose of the present study was to develop an optimized gastric floating drug delivery system (GFDDS) containing domperidone as a model drug. Box-Behnken design was employed in formulating the GFDDS with three polymers: hydroxypropyl methylcellulose K4M (HPMC K4M) (X1), Carbopol 934P (X2) and sodium alginate (X3), as independent variables. Floating lag time (FLT), total floating time (TFT), time required to release 50% of the drug (t50) and diffusion exponent (n) were selected as dependent variables. Seventeen formulations were prepared, dissolution data obtained was fitted to the power law and floating profiles were analyzed. HPMC loading was found to be significant for floating properties. Carbopol loading had a negative effect on floating properties but was found helpful in controlling the release rate of the drug. No significant effect of sodium alginate on floating properties was observed but it was important for gel formation. The quadratic mathematical model developed could be used to predict formulations with desired release and floating properties.

Statistical optimization of gastric floating system for oral controlled delivery of calcium.

The development of an optimized gastric floating drug delivery system is described. Statistical experimental design and data analysis using response surface methodology is also illustrated. A central, composite Box-Wilson design for the controlled release of calcium was used with 3 formulation variables: X1 (hydroxypropyl methylcellulose [HPMC] loading), X2 (citric acid loading), and X3 (magnesium stearate loading). Twenty formulations were prepared, and dissolution studies and floating kinetics were performed on these formulations. The dissolution data obtained were then fitted to the Power Law, and floating profiles were analyzed. Diffusion exponents obtained by Power Law were used as targeted response variables, and the constraints were placed on other response variables. All 3 formulation variables were found to be significant for the release properties (P <.05), while only HPMC loading was found to be significant for floating properties. Optimization of the formulations was achieved by applying the constrained optimization. The optimized formulation delivered calcium at the release rate of 40 mg/hr, with predicted n and T50% values at 0.93 and 3.29 hours, respectively. Experimentally, calcium was observed to release from the optimized formulation with n and T50% values of 0.89 (+/- 0.10) and 3.20 (+/- 0.21) hours, which showed an excellent agreement. The quadratic mathematical model developed could be used to further predict formulations with desirable release and floating properties.

A simple procedure for solving a continuous quadratic mathematical model

A new efficient procedure for solving a class of continuous linearly constrained quadratic problems is presented. It is based on the use of surrogate multipliers to construct an equivalent knapsack problem that is easier to solve, and a greedy-like procedure to solve it. This procedure is applicable in developing efficient branch and bound algorithms, by computing upper (lower) bounds for a quadratic integer problem.

Distillation under moderately high vacuum, illustrated by the vacuum distillation of zinc from lead

Based on the molecular interaction volume model (MIVM), the vapor–liquid phase equilibrium of Sn–Sb alloy was calculated, which was used to predict the element distribution of Sn–Sb alloy between vapor and liquid phase during vacuum distillation. A central composite design (CCD) was used to optimize the process parameters influencing the content of Sn in liquid phase and the direct yield of Sn. The studied parameters were distillation temperature, feeding materials and soaking time. Two quadratic mathematical model equations were derived for predicting the content of Sn in liquid phase and the direct yield of Sn. The analysis of variance (ANOVA) shown that distillation temperature was the most significant factor affecting the separation of Sn–Sb alloy. In the process optimization, while the direct yield of Sn equal to 92%, the maximum content of Sn in liquid phase should be 99.66 wt.% under the conditions of 1531 K, 137 g and 46 min. The confirmation test values of 91.22% and 99.43 wt.% were fair agreement with the predicted data, which demonstrated that these models were very good and can be used for parameter optimization in vacuum distillation.