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In this paper we prove Gårding's inequality for linear differential operators in generalized divergence form which satisfy a generalized Ehrling inequality, an ellipticity condition and a condition on the coefficients. Using a compact imbedding between certain anisotropic Sobolev spaces we...
2 be normed linear spaces andS:F
2 a linear operator on a balanced subsetF
1. IfN denotes a finite dimensional linear information operator onF
0, it is known that there need not be alinear algorithmφ:N(F
2 which is optimal in the sense that ‖φ(N(f)) −S(f‖ is...
A comparative study of the functional equationsf(x+y)f(x−y)=f
2(y/2)} which characterise the sine function has been carried out. The zeros of the functionf satisfying any one of the above equations play a vital role in the...
2–3 graphs in which each vertex is adjacent to at least two vertices of degree 3 are shown to be characterised by the number of vertices of degree 3 adjacent to vertices of degree 3 only.
A class of plane multigraphs having a series-parallel structure is defined and enumerated. The enumeration is carried out both for the rooted graphs as originally defined, and also for those where no distinctions are made between the vertices. Some other related problems are also discussed.
The symmetry of tensors, such as the symmetric or antisymmetric ones (built on a finite-dimensional complex vector space) may be described by a complex-valued homomorphism of the symmetric group with the specification that its action equal scalar multiplication by the value, e.g. by 1 or sign....
A multiplicative design is a family ofn subsets of ann-set whose incidence matrixA satisfiesA
whereα is a positive real vector andD is a positive diagonal matrix. This is a generalization ofλ-designs whereα is a constant vector and of (v, k, λ)-designs whereD is additionally...
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