Recursive method for inversion of lower triangular matrix

Algorithm for finding by recursion, the inverse of a lower triangular matrix of order n is developed, using its last row and the sub matrix obtained by deleting the last row and last column. In these algorithms the hitherto using double suffix notation for the entries of amatrix is replaced by single suffix notation. The necessary results are established

Barbell back squat:How do resistance bands affect muscle activation and knee kinematics?

ObjectivesThis study aimed to determine whether looped resistance bands affect knee kinematics and lower body muscle activation during the barbell back squat.MethodsTwenty-six healthy participants (13 female, 13 male) calculated their one repetition maximum (RM) prior to data collection. Each participant performed three squats at both 80% and 40% 1RM wearing a light resistance band, an extra-heavy resistance band and no resistance band.Vicon 3D motion analysis cameras were used to collect the kinematic data, and Delsys Trigno Lab wireless electromyography (EMG) system was used to measure vastus medialis, vastus lateralis, gluteus maximus, gluteus medius and biceps femoris muscle activity. Peak knee flexion angle, peak knee valgus angle and maximum tibial rotation values were examined. Peak EMG values were also analysed after being normalised and expressed as a percentage of maximum voluntary contraction (MVC).ResultsGluteus maximus (GM) activity is significantly increased when a resistance band is used during squatting. However, squatting with a resistance band is detrimental to knee kinematics as it leads to an increase in knee valgus angle and maximum tibial rotation angle. A direct correlation is recorded between an increase in resistance and an increase in these two angles.ConclusionsSquatting with resistance bands is likely to increase the risk of knee injury. Coaches and clinicians who already implement this technique are advised to remove resistance band squats from training and rehabilitation programmes. Further research evaluating the long-term effects of using resistance bands during the barbell back squat should be considered

Stability of a three species ecological system consisting of prey- predator species and a third species which is a host to the prey and enemy to the predator

Prey-Predator ecological system was presented by Lotka and Volterra in their classical model. Inspired by that, several researchers made significant contributions in this area by considering various special types of interactions between the prey and the predator. This has been the motivation for others in bringing a third species into the system thus forming a three species ecological system. Recently, some researchers worked on this three species system by considering interactions like Prey-Predator, Commensal -Host, Ammensal-Enemy, between the three species, which motivated the present paper. In this paper we discussed a three species ecological system consisting of a Prey (S1), a Predator (S2) and a third species (S3) which is a host to the prey and enemy to the predator.  Hence the prey plays Commensal for the third species and the predator plays Ammensal for the same. The mathematical model consists of three equations which constitute a set of three first order non-linear simultaneous differential equations in N1, N2 and N3, which are respective populations of the species S1, S2 and S3.The Equation for the third species is non-linear but decoupled with the prey-predator pair. Totally, eight equilibrium points of the model are identified and the criteria for their local stability are discussed. Solutions for the linearized perturbed equations are found and the results are illustrated.&nbsp

Mécanismes d'élimination de l'azote et du phosphore dans un chenal algal à haut rendement

Le devenir de l'azote(N) et du phosphore (P) a été étudié dans un chenal à haut rendement (CAHR) au cours de la période d'adaptation puis en phase stationnaire. En moyenne, la part de N total perdue atteint 34,5% du N admis en période d'adaptation et 24,5% en phase stationnaire tandis que la part assimilée par les algues atteint respectivement 32 et 43,5%. L'azote organique particulaire s'accumule dans le sédiment et subit une minéralisation lente pendant la phase d'adaptation puis rapide en phase stationnaire. Les pertes nettes en N dans le CAHR seraient dues à la sédimentation et à la volatilisation de NH3 en saison froide et seulement au dernier mécanisme, en saison chaude. Le bilan de l'azote ammoniacal en phase stationnaire montre que l'importance de la biomasse algale produite en saison chaude ne peut s'expliquer qu'en présence d'une minéralisation active du sédiment. Le taux de minéralisation est estimé à 12,4 kg N ha-1 j-1 en saison chaude contre 1,3 en saison froide. En moyenne, la part du P total perdue atteint 27% du P admis en période d'adaptation et 17,5% en phase stationnaire alors que la part assimilée par les algues atteint respectivement 25 et 17,5%. En phase stationnaire, l'élimination du P soluble dans le CAHR serait due à l'assimilation algale (54%) et à la précipitation chimique sous forme de sels de phosphates (46%).The fate of nitrogen (N) and phosphorus (P) was studied in a high-rate algal pond (HRAP) during the start-up period and under steady-state conditions. The HRAP was first used by Oswald and co-workers in Berkeley (California, USA) in the late 1950s for wastewater treatment with algae collection as a by-product for Single Cell Protein production. The HRAP consisted of a raceway shaped, shallow pond (less than 0.50 m deep) equipped with a continuous and gentle mixing device (paddle wheel) generally operated at 8 rpm. The paddle wheel is not used for aeration purposes.In this study, the HRAP is included in a wastewater treatment plant aimed at producing good quality effluent for agriculture reuse purposes. The treatment plant includes three components with the HRAP placed in the middle of the pond train. Up-stream, there is a two-phase anaerobic reactor (TAR) and downstream, two maturation ponds in series. Assigned removal tasks for the plant components are as follows: i) organic matter, suspended solids and helminth eggs for the TAR; ii) N and P for the HRAP; and iii) fecal coliforms for the two maturation ponds. The capacity of the plant is 1,500 inhabitants (70 m3/day), total hydraulic retention time is 8 days and the total occupied area is 1,500 m2 including walkways and other facilities. The plant was constructed in December 1996 and has been continuously operated since that time.The present paper focuses on the fate of N and P in the HRAP in order to evaluate its performance and to shed light on the mechanisms behind N and P removal, with the ultimate goal to improve surface and groundwater protection from pollution by wastewater nutrients. Under steady-state conditions and when we consider the soluble part of N and P taken up by the algal cells together with that lost (either by stripping or chemical precipitation), the total removal averaged 70% for N and 40% for P. Such important removal must be highlighted especially because the system relies on solar energy with no electromechanical aeration, is cheap to construct and easy to operate and maintain.To understand the mechanisms behind such a performance and also to gain experience for the process start-up and for rational operation and maintenance of future plants, an in-depth analysis on the fate of N and P was done based on the four-year follow up data. Total N losses reached an average of 34.5% in the start-up period and 24.5% under steady-state conditions, whereas N assimilated by the algae represented 32 and 43.5%, respectively. Particulate organic nitrogen (PON) accumulated in the bottom of the unit did undergo rapid mineralization under steady-state conditions. Mechanisms involved in N losses might be attributed to settling of PONr and, to much lesser extent, NH3 volatilization in the cold season, whereas the latter mechanism might occur primarily in the hot season. The rates of mineralization of HRAP sediment were estimated to be 12.4 and 1.3 kg of N ha-1 d-1 respectively for the hot and the cold season.On average, total P losses in the HRAP reach 27% in the start-up period and only 17.5 % under steady-state conditions, whereas algae assimilation represented 25 and 17.5% respectively. Under steady-state conditions, algae uptake (54%) and chemical precipitation (46%) were found to be the main mechanisms for P removal in the HRAP

Kinetics & Mechanism of Reaction of 4-t-Butylphenol with Formaldehyde Using Alkali Catalysts

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Spectrophotometric Studies of 2-Methylol-4- tert-butylphenol- Fe(III) Complex

255-25