DIAGONALLY COMPENSATED REDUCTION AND MULTISPLITTING OF A SYMMETRIC POSITIVE DEFINITE MATRIX

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Strict regular completions of Cauchy spaces

A diagonal condition is defined and used in characterizing the Cauchy spaces which have a strict, regular completion.

     

Nonnegative tensors revisited: plane stochastic tensors

In this paper, we develop and enrich the theory of nonnegative tensors. We define the sign nonsingular tensors and establish the relationship between the combinatorial determinant and the permanent of nonnegative tensors. We generalize the results from doubly stochastic matrices to totally plane stochastic tensors and obtain a probabilistic algorithm for locating a positive diagonal in a nonnegative tensor under certain conditions. We form a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors. We obtain a lower bound for the minimum of the axial N-index assignment problem by means of the set of plane stochastic tensors.     

B-DNA Structure and Stability: The Role of Nucleotide Composition and Order

We have quantum chemically analyzed the influence of nucleotide composition and sequence (that is, order) on the stability of double-stranded B-DNA triplets in aqueous solution. To this end, we have investigated the structure and bonding of all 32 possible DNA duplexes with Watson–Crick base pairing, using dispersion-corrected DFT at the BLYP-D3(BJ)/TZ2P level and COSMO for simulating aqueous solvation. We find enhanced stabilities for duplexes possessing a higher GC base pair content. Our activation strain analyses unexpectedly identify the loss of stacking interactions within individual strands as a destabilizing factor in the duplex formation, in addition to the better-known effects of partial desolvation. Furthermore, we show that the sequence-dependent differences in the interaction energy for duplexes of the same overall base pair composition result from the so-called “diagonal interactions” or “cross terms”. Whether cross terms are stabilizing or destabilizing depends on the nature of the electrostatic interaction between polar functional groups in the pertinent nucleobases.