Variable-step (VS) second derivativek -step 3-stage Hermite-Birkhoff-Obrechkoff (HBO) methods of orderp= (k+3), denoted by HBO (p) are constructed as a combination of lineark -step methods of order (p- 2) and a second derivative two-step diagonally implicit 3-stage Hermite-Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for considering this class of formulae is to obtain a set of k -step methods which are L -stable and are suitable for the integration of stiff differential systems whose Jacobians have some large eigenvalues lying close to the imaginary axis with negative real part. The approach, described in the present paper, allows us to developL -stable k -step methods of order up to 10. Selected HBO (p) of order p, p=9; 10, compare favorably with existing Cash L-stable second derivative extended backward differentiation formulae, SDEBDF (p), p=7; 8 in solving problems often used to test stiff ODE solvers.

Predictor-corrector (PC) methods for the numerical solution of stiff ODEs can be extended to include the second derivative of the solution. In this paper, we consider second derivative PC methods with the three-step second derivative Adams-Bashforth as predictor and two-step second derivative Adams-Moulton as corrector which both methods have order six. Implementation of the proposed PC method is discussed by providing Nordsieck representation of the method and preparing an starting procedure, an estimate for local truncation error and a formula for changing stepsize. Efficiency and capability of the method are shown by some numerical experiments.

Background: Common variable immune deficiency (CVID) is the commonest symptomatic primary immunodeficiency and represents a heterogenous collection of disorders resulting mostly in antibody deficiency and recurrent infections. The syndrome includes impaired B-cell maturation, impaired somatic hyper mutation, reduced numbers of circulating memory and isotype-switched memory B cells, and absent or reduced plasma cells. B cell maturation antigen (BCMA) is a tumor necrosis family receptor superfamily member 17 (TNFRSF17), expressed only on B cell lines, and is essential for survival of long-lived plasma cells. The aim of this study was to evaluate mutations in BCMA in patients with CVID in compare with normal individuals in Isfahan, Iran.Methods: Blood samples were collected from 10 CVID patients with substitutive immunoglobulin therapy before immunoglobulins (Ig) infusion and 10 normal controls in ethylenediaminetetraacetic acid (EDTA) tubes then DNA samples were extracted and after the polymerase chain reaction (PCR) was done, samples were sequenced.Findings: After reviewing the results of the sequence and alignment of the sequences, no mutations in the gene were seen.Conclusion: In addition to the study of mutation in BCMA gene, BCMA gene and protein expression level should be considered to understand more aspects of this disease.

The Effect of different culture conditions on growth and production of antimicrobial agents by Oudemansiella spp, using the Variable Size - Simplex Design, were investigated. The results obtained from the experiments indicated that the optimum condition for growth and production of antimicrobial agents, situated at pH between 5.6 and 6.8, temperature between 28°C and 30.6 ºC, shaking rate between 137 and 170 rpm. The results also showed the fungus grow and produced antimicrobial agents at a very wide range of glucose concentration. Increasing the concentration of glucose over 15 g/L, resulted in decreasing the activity of the fungus.

In this paper, in continuation of the construction of efficient numerical methods for stiff IVPs, we construct type two Nordsieck second derivative general linear methods with order p = s, where s is the number of internal stages, and stage order q = p. Implementation of the constructed methods with fixed and variable stepsize is discussed which verifies their efficiency.

Dynamic Analysis of an axially moving cable with time dependent tension and velocity is studied in this paper. Tension force and the moving speed are assumed to be harmonic. It is found that there exists a specific value of speed in which natural frequency of the system approaches zero. This specific speed for such a critical condition is called critical speed and it will be proved that increasing the cable tension increases critical speed of the moving cable. Multiple-Scales perturbation technique is used to discretize the nonlinear equations of motions. Critical speeds are then obtained in which vibrations of motion become unstable. Stability analysis is carried out for different sets of excitation frequency. Dynamic responses of the system are calculated using Galerkin’s method. A comprehensive parametric study is carried out and effects of different parameters like the moving speed and tension force on the responses are studied both in frequency and time domain.