DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA KEITHCONRAD

De
Publicado por

  • expression écrite
DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA KEITH CONRAD 1. Introduction We develop some results about linear differential equations with constant coefficients using linear algebra. Our concern is not cookbook methods to find all the solutions to a differential equation, but the computation of the dimension of the solution space. Consider a homogeneous linear differential equation with constant (real) coefficients: (1.1) y(n) + an−1y (n−1) + · · ·+ a1y ′ + a0y = 0.
  • basis of ker
  • real vector space
  • complex vector space
  • zero function
  • differential equations
  • linear algebra
  • order
  • solution
Publicado el : miércoles, 28 de marzo de 2012
Lectura(s) : 58
Fuente : cibia8peru.org
Número de páginas: 4
Ver más Ver menos
EFFECT OF HIGH HYDROSTATIC PRESSURES ON QUALITY INDICES AND MICROBIOLOGICAL INACTIVATION OF ALOE VERA (Aloe barbadensis Miller) GEL EFECTO DE ALTAS PRESIONES HIDROSTATICAS SOBRE INDICES DE CALIDAD Y CRECIMIENTO MICROBIANO DE ALOE VERA (Aloe barbadensis Miller) GEL a,b aa c Antonio VegaGálvez, Claudia Giovagnoli , Mario PérezWonJudith, Gipsy TabiloMunizaga , a ad,e Vergara , Margarita Miranda , Karina Di Scala a Department of Food Engineering, Universidad de La Serena. Av. Raúl, Bitrán s/n, 599, La Serena. Chile. Email: avegag@userena.cl b CEAZA, Center for Advanced Studies in Arid Zones, Universidad de La Serena, Av. Raúl Bitrán s/n, Box 599, La Serena. Chile. c Department of Food Engineering, Universidad del BioBío, Chillan, Chile. d Food Engineering Research Group, Facultad de Ingeniería, Universidad Nacional de Mar del Plata. Av. Juan B. Justo 4302, Mar del Plata, Argentina. e CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas), Argentina. RESUMEN El objetivo de este trabajo fue estudiar el efecto de altas presiones hidrostáticas (300500 MPa/15 min) sobre los índices de calidad del A. vera gel incluyendo capacidad antioxidante, vitamina C, firmeza y crecimiento microbiano después de 60 días de almacenamiento refrigerado. A 300 y 400 MPa se observó una disminución significativa en la capacidad antioxidante (DPPH) comparado con la muestra control (p<0.05). Entre las muestras presurizadas, la retención de la Vitamina C mostró su máximo valor a 500 MPa (p<0.05). Las muestras tratadas a 300 y 500 MPa aumentaron su textura con respecto al valor inicial y los valores fueron similares (p<0.05). El tratamiento a 300 MPa presentó una notable disminución en microorganismos aeróbicos mesófilos y levaduras, comparados con las muestras no tratadas. Basados en la aplicación delmodelo de Gompertz se pudo estimar una vida útil de 26 días para las muestras de A. vera gel. Trabajar a presiones de 400 and 500 MPa redujo el contenido de microorganismos hasta valores no detectables. SUMMARY The aims of this work were to study the effect of high hydrostatic pressures (300500 MPa/15 min) on quality indices of A. vera gel including antioxidant capacity, vitamin C, firmness and microbiological grow after 60 days of refrigerated storage. At 300 and 400 MPa a significant decrease in antioxidant capacity was noted compared to control sample. DPPH (p<0.05) and retention of Vitamin C (p<0.05) showed maximum values at 500 MPa among pressurized samples. Samples treated at 300 and 500 MPa increased initial firmness presenting similar values (p<0.05). Treatment at 300 MPa presented a notable decreased in meshophilic aerobic microorganisms and yeasts, compared to nontreated samples. Applying the Gompertz model, a shelf life of 26 days was estimated for A. vera gel samples. Working at 400 and 500 MPa reduced microorganisms until undetectable levels. Keywords:high hydrostatic pressures, quality indices, microbiological growth; shelf life, Aloe vera gel INTRODUCTION2007). In order to extend its shelf life it becomes imperative to process it to maintain A. veragel (Aloe Barbadensis Milleralmost all the bioactive chemicals naturally) use has increased due to its therapeutic andpresent in the plant during processing. In this functional properties (Miranda et al., 2009).sense, the application of high hydrostatic The chemical composition of the gel includespressure (HHP) replaces conventional phytochemicals like polyphenolicstechniques of food production (Rastogi, compounds and ascorbic acid with highAngersbach & Knorr, 2000; VegaGálvez et antioxidant capacities which are able toal., 2011). HHP application success by gentle reduce the free radicals that cause oxidationmicrobial inactivation and improvement of reactions (Serrano et al., 2006; Vega et al.,mass transfer processes. Moreover, changes
in food texture during HHP are strongly related to transformations in cell wall polymers due to enzymatic and non enzymatic reactions, being a major challenge to use this novel technology to adjust raw materials, ingredients and processes to improve texture of processed plant based foods (Sila et al., 2008). Therefore, the aim of this work was to study the effect of high hydrostatic pressure on quality indices ofA. veragel including antioxidant capacity, vitamins C and texture as well as microbiological growth after 60 days storage. MATERIALS AND METHODS Sample preparation and high hydrostatic pressure treatmentA. veraprovided by the INIAIntihuasi, were Coquimbo  Chile. Homogenous leaves were selected according to size, color and freshness. Acibar (a yellow colored liquid) was extracted by cutting the base of the leaves and allowing them to drain vertically for 1 h. The epidermis was then separated from the gel, which was extracted and triturated by a Phillips Electric blender (HR1720, Amsterdam, The Netherlands). Packaged samples were placed in a cylindrical loading container at room temperature and pressurized at 300, 400 and 500 MPa during 1, 3 and 5 min for each treatment and compared to untreatedA. veragel (control). Water was employed as pressuretransmitting medium, working at 17 MPa/s ramp rate; decompression time was less than 5 s. A 2 L processing unit (Avure Technologies Incorporated, Kent WA, USA) was used to pressurize the aloe samples. Then, they were removed and vacuum sealed in low density polyethylene bags for storage. Pressurized samples were stored at 4ºC. Quality and microbiological analyses were performed at 0 and 60 days storage. Quality parameters Microbiological analysis Samples were analyzed for numbers of mesophilic aerobic microorganisms (MAM) and moulds and yeasts (MY). Twenty five mL or grams of each sample were obtained aseptically and homogenized with a 225 mL peptone saline solution 0.1% (Difco, Detroit, USA.) in a filter stomacher bag using a Stomacher® (Biocheck, S.A., Barcelona, Spain) at 240 rpm for 60 seconds. Further decimal dilutions were made with the same diluent, and duplicates of at least three appropriate dilutions were plated on
appropriate media. In order to enumerate the mesophilic aerobic microorganisms, 1 mL of each dilution was pourplated in Plate Count Agar (PCA, Difco, Detroit, USA.). After incubation at 30°C for 72 h, plates with 30 300 colonies were counted. To counts the 1 moulds and yeasts, 1 mL of the initial (10) dilution was spread plated on three olates of Dicloran Rose Bengal Chloramphenicol (DRBC, Difco, Detroit, USA.) agar, and 0.1 mL of each subsequent was spread on one DRBC plate. Plates were then incubated at 25°C for 35 days, and plates with 30300 colonies were counted. Microbial data were transformed into logarithms of the number of colonyforming units (log CFU/mL). Detection limit was 10 CFU/mL according to Geneva (1999). Microbial growth curve modeling
The experimental data obtained were fitted to the reparameterized version of the modified Gompertz equation, Eq. 1 (Briones et al., 2010).
Eq.1 where N(t) is the viable cell concentration at time t. A is related to the difference decimal logarithm ofmaximum bacterialgrowth attained at the stationary phase and decimal logarithm ofthe initial value of cell concentration, µmaxthe maximal specific is growth rate, λ is the lag time, Nmaxthe is microbial threshold value, SL is the microbiological acceptability limit (i.e., the time at which N(t) is equal to Nmax), and t is the storage time. The modified Gompertz equation was fitted to microbial data using the nonlinear regression modulus of the GraphPad Prism v. 4.03 (GraphPad Software, Inc., San Diego, CA, USA). The goodness of fit was evaluated using the 2 coefficient of determination (R). Determination of DPPH radical scavenging activity Free radical scavenging activity of the samples was determined using the 2,2 diphenyl2picrylhydrazyl (DPPH) method (Turkmen et al., 2005). Total antioxidant activity (TAA) was expressed as IC50, which is the concentration required to obtain a 50%
antioxidant capacity. IC50 wasdetermined from a graph of antioxidant capacity (%) against extract concentration (μg/mL sample). Determination of Vitamin CLascorbic acid was determined by the 2,6 dichlorophenolindophenol (Merck KGaA, Darmstadt, Germany) titrimetric method. A total of 10 ± 0.1 g of triturated sample were weighed, filtered, and diluted to a volume of 50 mL. All measurements were done in triplicate. Vitamin C content was expressed as mg Vit C/100 g d.m.Determination of firmness Firmness of samples was measured using a Texture Analyzer (Texture Technologies Corp., TA, XT2, Scardale, NY, USA). The puncture diameter was 2 mm, with a travel distance of 20 mm and 1.7 mm/s test speed. The maximum force was measured by making one puncture in each sample, using 10 slabs per treatment. Results were expressed as N/mm. Statistical analysis Twoway analysis of variance (ANOVA) (Statgraphics Plus® 5.1 software, Statistical Graphics Corp., Herndon, USA) was used to indicate significant differences among samples. Significance testing was performed using Fisher's least significant difference (LSD) test; differences were taken as statistically significant (p<0.05).
RESULTS AND DISCUSSION Effect on microbiological behavior: application of Gompertz equation The initial microbial load of freshA. veragel was 1.95 ± 0.048 and 2.37 ± 0.140 log CFU/mL for aerobic mesophilic microorganisms (AMM) and yeasts (Y), respectively. Moulds were not detected. Untreated samples did not verified the microbiological requirements according to OMS (AMM >2.0 log CFU/mL; Y >2.0 log CFU/mL). In the case of samples treated at 300 MPa during 3 and 5 min, they presented microbiological growing at the end of the storage (60 days). See Figure 1. Data for yeasts are not shown. In addition, samples treated at 400 and 500 MPa during 1, 3 and 5 min presented undetectable levels of microorganisms’ counts.When adjusting the experimental microbial data to the Gompertz equation (Eq 1), the following kinetic parameters estimations for
the maximum specific growth rate (μmax), lag phase(λ) and the shelf life (SL) for the aerobic mesophilic microorganisms and yeasts counts ofA. verasamples were gel obtained. For AMM: SL= 26.13 days, µmax= 1 0.13 daysand=14.49 days; and for 1 yeasts: SL= 26.19 days, µmax= 0.12 days and=13.15 days. Therefore, for 300 MPa1 min, the modified Gompertz equation was 2 able to describe microbial AMM (R= 0.95) 2 and Y growth (R= 0.95). The microbial shelf life estimated forA. vera geltreated at 300 MPa/1min was 26 days for both AMM and Y. Based on previous microbiological results, the analysis of quality attributes was focused on the effects of HHP (300, 400 and 500 MPa) during 5 min of processing.
Figure 1. Effect of pressure (300 MPa/1 min) on mesophilic aerobic microorganisms ofA. vera2 gel. (R=0.95) Effect on DPPHradical scavenging activity Initial content of DPPH was 37392.95± 2822.05 µg/mL. A significant decrease in antioxidant activity was noted in all pressurized gel samples compared to the control sample. The treatment at 400 MPa showed the maximum reduction compared to the samples treated at 300 and 500 MPa. Moreover, the highest antioxidant capacity, between pressurized samples was observed at 500 MPa. See Figure 2. Effect onVitamin C The initial vitamin C was 127.59 mg/100 g d.m. The retention of vitamin C after storage for 60 days at 4ºC was 60% at 300 MPa, 93 % at 400 MPa and 81% at 500 MPa (p<0.05). See Figure 2.
Effect on firmness Samples pressurized at 300 and 500 MPa showed the same final firmness of the samples (p<0.05). On the other hand, working at 400 MPa showed similar firmness when compared to fresh samples.
Figure 2. Effect of pressure on DPPH and Vitamin C ofA. veragel. after 60days storage. Identical letters above the bars indicate no significant difference (P < 0.05). CONCLUSIONS Effects of hih hdrostatic ressure treatments 300500MPa/ 15 minon ualit attributes as well as microbiolo icalrowth were investiated in this work. Microbial data was successfullfitted to the modified Gompertz equation. The hi hest antioxidant ca acitincludin DPPHbetween pressurized samples was observed at 500 MPa P<0.05. All treatments decreased initial vitamin C content beinthe lowest values that at 300 MPa. HHP also had si nificanteffect on the firmness of the sam ledue to chanes in cell structure because ofrocessin P<0.05. Based on these results, workinat 500 MPa/5 min could reservethe most relevantualit attributes ofA. vera elincludin microbiolo ical, nutritionalVitamin Cand h sicochemicalaspects antioxidant capacity and texture). REFERENCES Briones, L.; Reyes J.; TabiloMunizaga, G.; PérezWon, M. (2010). Microbial shelflife extensión of chilled Coho salmon (Oncorhynchus kisutch) and Abalone (Haliotis rufrescens) by high hydrostatic pressure treatment. Food Control. 21: 1530 1535.
WHO, World Health Organization, Geneva. (1999). Monographs on selected medicinal plants. Vol. 1. Miranda, M.; Maureira, H.; Rodríguez, K.; VegaGálvez, A. (2009). Influence of temperature on the drying kinetics, physicochemical properties, and antioxidant capacity of Aloe Vera (Aloe Barbadensis Miller) gel. Journal of Food Engineering, 91: 297304. Rastogi, N.K.; Angersbach, A.; Knorr, D. (2000). Synergistic effect of high hydrostatic pressure pretreatment and osmotic stress on mass transfer during osmotic dehydration. Journal of Food Science, 45 : 2531. Serrano, M.; Valverde, J.M., Guilleän, F.; Castillo, S.; MartínezRomero, D., Valero, D. (2006). Use of Aloe vera Gel Coating Preserves the Functional Properties of Table Grapes. Journal of Agricultural and Food Chemistry, 54: 38823886. Sila, D.N.;Duvetter, T.;De Roeck, A.;Verlent, I.;Smout, C.,Moates, G.K.; Hills, B.P.; Waldron, K.K.;Hendrickx, M.; Van Loe, A. (2008). Texture changes of processed fruits and vegetables: potential use of highpressure processing. Trends in Food Science and Technology, 19(6): 309 319. Turkmen, N.; Sari, F.; Velioglu, Y.S. (2005). The effect of cooking methods on total phenolics and antioxidant activity of selected green vegetables. Food Chemistry, 93: 713 718. Vega, A.; Uribe, E.; Lemus, R.; Miranda, M. (2007).Hotair drying characteristics of Aloe vera (Aloe barbadensis Miller) and influence of temperature on kinetic parameters. LWT Journal Food Science and Technology, 40: 16981707. VegaGálvez, A.; Uribe, E.; Perez, M.; Tabilo Minizaga G.; Vergara J.; GarciaSegovia, P.; Lara, E.,Di Scala, K. (2011). Effect of high hydrostatic pressure pretreatment on drying kinetics, antioxidant activity, firmness and microstructure of Aloe Vera (Aloe Barbadensis Miller) gel. LWT Food Science and Technology, 44(2): 384391.
¡Sé el primero en escribir un comentario!

13/1000 caracteres como máximo.

Difunda esta publicación