On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains.Â

Taguchi Method for Investigating the Performance Parameters and Exergy of a Diesel Engine Using Four Types of Diesel Fuels

The effects of changes in engine operating parameters, i.e., engine speed, throttle and water temperature, for four types of diesel fuel (A, B, C and D) of different specific gravities, as supplied from local market and refineries, were studied and simultaneously optimized. The experiment design was based on Taguchi’s “L' 16” orthogonal table, and the engine was put to test at different engine speeds, throttling opening percentages and water temperatures, using different fuels. The data were analyzed using S/N (signal to noise ratio) for each factor. The obtained results show that the optimum operating conditions for minimum BSFC (brake specific fuel consumption) are achieved when the engine speed is 2500 rpm, the throttle is placed at 75% of full throttling, the water temperature is 80 oC and the engine is using fuel type D. Also, results of S/N ratio reveal that the throttle has significant influence on brake thermal and exergic efficiencies. Water temperature is the second most effective factor and then comes the influence of engine speed. The least effective factor among the studied parameters for the types of fuel considered in this experiment is the fuel type

Feedlot performance of Sudanese desert lambs fed with mash or pelleted diet of varying energy levels

AbstractThis experiment was conducted using 18 Sudan desert ram lambs (22±5.7kg) to examine the effects of feeding with diets of different energy levels and physical forms on feedlot performance. These lambs were randomly divided into three feed groups of six animals each in a completely randomized design (CRD). Following an acclimatization period of three weeks, three experimental diets were offered, each for one group. High Energy Pellets (HEP) and High Energy Mash (HEM) diets (10.50MJME/kg DM) of a pelleted and mash form, respectively and Low Energy Diets (LEP) was a pelleted and low energy diet (8.5MJME/kg DM).The experiment continued for all diets to an average 40kg live weight lamb. Results revealed lower Dry Matter Intake (DMI) (P>0.001), improved Feed Conversion Ratio (FCR) (P<0.01) and higher Average daily gain (ADG) (P<0.01) for the high energy groups compared to the low energy diet group. No significant (P>0.05) differences were observed due to pelleting between the two higher energy groups. No significant (P>0.05) differences were observed among treatment groups in the Metabolizable Energy (ME) required to put a unit of body weight gain

Coalescing Fiedler and core vertices

The nullity of a graph G is the multiplicity of zero as an eigenvalue in the spectrum of its adjacency matrix. From the interlacing theorem, derived from Cauchy’s inequalities for matrices, a vertex of a graph can be a core vertex if, on deleting the vertex, the nullity decreases, or a Fiedler vertex, otherwise. We adopt a graph theoretical approach to determine conditions required for the identification of a pair of prescribed types of root vertices of two graphs to form a cut-vertex of unique type in the coalescence. Moreover, the nullity of subgraphs obtained by perturbations of the coalescence G is determined relative to the nullity of G. This has direct applications in spectral graph theory as well as in the construction of certain ipso-connected nano-molecular insulators.peer-reviewe

Nullity of a graph with a cut-edge

The nullity of a graph is known to be an analytical tool to predict reactivity and conductivity of molecular π-systems. In this paper we consider the change in nullity when graphs with a cut-edge, and others derived from them, undergo geometrical operations. In particular, we consider the deletion of edges and vertices, the contraction of edges and the insertion of an edge at a coalescence vertex. We also derive three inequalities on the nullity of graphs along the same lines as the consequences of the Interlacing Theorem. These results shed light, in the tight-binding source and sink potential model, on the behaviour of molecular graphs which allow or bar conductivity in the cases when the connections are either distinct or ipso.peer-reviewe

Pharmacodynamics Drug Interactions of Metformin with Aspirin and Nifedipine

Metformin is now being recognized as the standard therapy in T2D patients who are overweight. Metformin has many drug-disease interactions that can increase the risk of metformin-associated lactic acidosis. Therefore this study was conducted to evaluate any possible pharmacodynamic interactions between metformin and drugs used to treat chronic diseases e.g. Hypertension. The rats were fasted overnight before inducing diabetes with streptozotocin. The rats were given an intraperitoneal injection of streptozotocin (50 mg kg−1) freshly prepared in 0.1M sodium citrate buffer. The diabetic state was confirmed 72 h after streptozotocin injection. Diabetic rats were grouped into seven groups each group of five rats and distributed among the normal control group diabetic control group and the treatment groups. The treatment continued for 10 days. Blood samples were taken before treatment and after 10 days and analyzed for serum glucose, cholesterol, HDL, LDL, and triglycerides. In the diabetic control group which was given STZ alone the blood glucose level decreased significantly (p &lt; 0.05) after 10 days but still above the hyperglycemic level (200mg/dl). The same was observed in the group treated with metformin. The group treated with nifedipine and aspirin showed significant reduction (p &lt; 0.01) in the glucose level below the hyperglycemic level (200mg/dl). While the groups treated with (Metformin + Nifedipine) and (Metformin +Aspirin) showed highly significant reduction (P&lt;0.001) in blood glucose level. These results conclude that the combination of (metformin +Nifedipine) and the combination of (Metformin + Aspirin) have highly significant hypoglycemic effect. It also showed that Nifedipine has promising role in reducing blood glucose level, lipid profile especially LDL-cholesterol, and body weight

Edge Degree Weight of Sequential Join of Graphs

Let the weight w of an edge e= uv={u,v} of a graph G be defined by w(e)=deg(u)+deg(v)-2 and the weight of G be defined by w(G)= ∑ e ∈ E(G)w(e), where E(G) is the edge set of G. In this paper the weights of joins, sequential joins, unions, intersections, and products (Cartesian and Tensor) of sets of graphs are obtained. This leads to a variety of open questions and new studies

Improvement on rooting quality of Jatropha curcas using indole butyric acid (IBA).

The effects of indole-3-butyric acid (IBA) concentrations and three types of cutting (softwood,semi hardwood and hardwood) on root performance of Jatropha curcas L. cuttings were investigated. Two experiments were conducted where in experiment 1, conducted on July 2007, the hardwood cutting gave the highest mean value for root dry weight (0.2g), number of roots (22) with percentage of rooted cuttings (56%) compared to the one using softwood cutting. 10, 000 mg/L IBA gave the highest mean value for root length (13.6cm), number of roots (28), percentage of rooted cuttings (74%) with root dry weight (0.5g). In experiment 2, conducted on January 2008, the hardwood cutting once again gave the highest mean value for root length (12.1cm) and root dry weight (0.4g). The greatest root number (59) was obtained at 20, 000 mg/L. There was no significant effect on percentage of rooted cuttings, root dry weight, root length and rootball diameter. The histological studies showed that adventitious roots were originated directly from the endodermis. The root primordial started to develop on day 8 and emerged through the epidermis after day 11