Problem statement: The lacunary interpolation problem, which we had investigated in this study, consisted in finding the six degree spline S(x) of deficiency four, interpolating data given on the function value and third and fifth order in the interval [0,1]. Also, an extra initial condition was prescribed on the first derivative. Other purpose of this construction was to solve the second order differential equations by two examples showed that the spline function being interpolated very well. The convergence analysis and the stability of the approximation solution were investigated and compared with the exact solution to demonstrate the prescribed lacunary spline (0, 3, 5) function interpolation. Approach: An approximation solution with spline interpolation functions of degree six and deficiency four was derived for solving initial value problems, with prescribed nonlinear endpoint conditions. Under suitable assumptions, the existences; uniqueness and the error bounds of the spline (0, 3, 5) function had been investigated; also the upper bounds of errors were obtained. Results: Numerical examples, showed that the presented spline function proved their effectiveness in solving the second order initial value problems. Also, we noted that, the better error bounds were obtained for a small step size h. Conclusion: In this study we treated for a first time a lacunary data (0,3,5) by constructing spline function of degree six which interpolated the lacunary data (0,3,5) and the constructed spline function applied to solve the second order initial value problems.

Purpose: To present the outcomes of treatment of Kienbock's Disease (KD) stage III, by excisional arthroplasty of lunate with Palmaris Longus (PL) tendon as a spacer. Methods: Twenty-one patients were diagnosed with KD stage III, 14 females, and 7 males. They were treated by excision of the lunate plus PL tendon ball as a spacer. Mean follow up period was 38 months (24-60). Pre- and post-operative treatment assessment were by recording the clinical examination data, the investigation by radiological imaging (plain and CT scan), MRI, and scoring of Disabilities of Arm, Shoulder and Hand (DASH) system. Results: Nineteen patients improved clinically to a great extent, by relieving symptoms, a better range of movement, functional satisfaction and no conspicuous Carpal Height Ratio (CHR) change. Mean DASH score improved from 38.5 to 6.8. Two patients had less favorable clinical outcome, yet, they were not interested to have further operations. Conclusions: Treatment of KD stage III by excisional arthroplasty plus palmaris longus tendon spacer is a low demand operation, which can be performed in a moderate hospital environment, and can accomplish good satisfactory results comparable to other more sophisticated, costly procedures. Type of study/Level of evidence: Prospective case series, level IV.