We report our initial experience in two patients using real-time three-dimensional echocardiography to assess perimembranous ventricular septal defect and device morphology and their relation with contiguous cardiac structure. Defect size and rims as well as device position and profile were displayed from the three-dimensional "en face" views. We think that real-time three-dimensional echocardi...

We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+ βyn)/(1 + yn−1) when the parameters α < 0 and β ∈ R. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1 = (a+ byn)/(A+Byn−1), when th...

The second order partial difference equation of two variables Du := A1,1(x)∆1∇1u+A1,2(x)∆1∇2u+ A2,1(x)∆2∇1u+ A2,2(x)∆2∇2u + B1(x)∆1u+ B2(x)∆2u = λu, is studied to determine when it has orthogonal polynomials as solutions. We derive conditions on D so that a weight function W exists for which WDu is self-adjoint and the difference equation has polynomial solutions which are orthogonal with respe...

The purpose of this study is to explore the learning environment and the learning technologies in a web environment. Our research is based on previous success with collaborative learning technology studies, which showed the objects should be the cores of the collaborative technologies. In keeping with this, our current research proposed a learning environment for collaborative learning, especia...

We apply the Hecke operators T (p) and T̃j(p 2) (1 ≤ j ≤ n, p prime) to a degree n theta series attached to a rank 2k Z-lattice L, n ≤ k, equipped with a positive definite quadratic form in the case that L/pL is hyperbolic. We show that the image of the theta series under these Hecke operators can be realized as a sum of theta series attached to certain closely related lattices, thereby generali...

We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint ...

— In this paper we give a characterization of primitive recursive functions ƒ : N~* N{r^0, s>0) and define a Hierarchy of classes b^O) of these functions by a syntactic measure ofeomplexity. The behavior ofthe classes J^a+b^ respect to different operators is also analyzed. The classes J^ + b coincide with the ones ofCleavé's hierarchy for a^2,b^0 and give a refinement of the Meyer-Ri...

In this paper, we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.

The family of orthogonal polynomials corresponding to a generalized Jacobi weight function was considered by Wheeler and Gautschi who derived recurrence relations, both for the related Chebyshev moments and for the associated orthogonal polynomials. We obtain an explicit representation of these polynomials, from which the recurrence relation can be derived.

A 4-year-old female presented with painless mass on left side of neck, biopsy of which was done from referring place. As the report was not available, FNAC of the mass was done, which was pleomorphic adenoma of left parotid gland. CT shows large heterogeneous mass in relation to the left parotid gland and mass was contiguous with the carotid artery. Parotidectomy was positive for malignancy. Hi...