But with President Boris Yeltsin ailing, there are signs conditions could worsen again _ the ruble is sliding, fuel shortages plague many regions and Russia is starved for the foreign loans that have kept it afloat for years.
2.
Note that for functions of three or more variables, the " determinant " of the Hessian does not provide enough information to classify the critical point, because the number of jointly sufficient second-order conditions is equal to the number of variables, and the sign condition on the determinant of the Hessian is only one of the conditions.
3.
Although this connection may appear superficial for a reader not familiar with differential equations, it is indeed the case that the main scale-space formulation in terms of non-enhancement of local extrema is expressed in terms of a sign condition on partial derivatives in the 2 + 1-D volume generated by the scale space, thus within the framework of partial differential equations.
4.
Specifically, sign conditions are imposed on the sequence of principal minors ( determinants of upper-left-justified sub-matrices ) of the bordered Hessian, the smallest minor consisting of the truncated first 2 " m " + 1 rows and columns, the next consisting of the truncated first 2 " m " + 2 rows and columns, and so on, with the last being the entire bordered Hessian.
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