We establish a sufficient condition for strict total positivity of a matrix. In particular, we show that if the (positive) elements of a square matrix grow sufficiently fast as their distance from the diagonal of the matrix increases, then the matrix is strictly totally positive.

A sufficient condition for secure ping–pong protocols is repretsented. This condition, called name– suffixing, is essentially to insert identities of participants in messages. We prove its sufficiency and discuss the feature of security in terms of name–suffixing.

Given a probability distribution {pi}i 1,2,...,W , that is, 0 ≤ pi ≤ 1 i 1, 2, . . . ,W and ∑W i 1 pi 1, the ordinary expectation value of a quantity Q of a system under consideration is defined by ∑W i 1 piQi, where W is the total number of accessible states and is enormously large in statistical mechanics, typically being 210 23 . In the field of generalized statistical mechanics for complex ...

Quantum discord characterizes "nonclassicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of nonzero quantum discord for any dimensional bipartite states. This condition is easi...

In Eurocrypt 2005, Wang et al. presented a collision attak on MD5. In their paper, they intoduced “Sufficient Condition” which would be needed to generate collisions. In this paper, we explain how to construct sufficent conditions of MD5 when a differential path is given. By applying our algorithm to a collision path given by Wang et al, we found that sufficient conditions introduced by them co...

We present explicit examples to show that the ‘compatibility criterion’ [recently obtained by us towards providing equilibrium configurations compatible with the structure of general relativity] which states that: for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), whereM is the total mass andR is the radius of the config...

In this paper, we study the stability of interval dynamical systems. A sufficient condition for the stability of a polytope of matrices, which is shown to be necessary and sufficient for a certain class of matrices, is obtained. The results developed can also be applied to the stability of a positive cone of matrices and sufficient conditions for the stability of interval dynamical systems are ...

Planar graphs without 3-cycles at distance less than 4 and without 5-cycles are proved to be 3-colorable. We conjecture that, moreover, each plane graph with neither 5-cycles nor intersecting 3-cycles is 3-colorable. In this conjecture, none of the two assumptions can be dropped because there exist planar 4-chromatic graphs without 5-cycles, as well as planar 4chromatic graphs without intersect...

output of M adds additional signal to the actuator, it may saturate the actuator easily even though the net effect of this Q controller in the ideal case is cancelled in the feedback loop. Another reason is that it is not clear how this structure can be used for fault-tolerant control.