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NEW PHYSICS RESEARCH HAS BEEN REPORTED BY SCIENTISTS AT YEREVAN STATE UNIVERSITY
Science Letter
July 15, 2008
According to a study from Yerevan, Armenia, "We provide an index
formula for solutions of variational inequality problems defined by a
continuously differentiable function F over a convex set At represented
by a finite number of inequality constraints. Our index formula can
be applied when the solutions are nonsingular and possibly degenerate,
as long as they also satisfy the injective normal map (INM) property,
which is implied by strong stability."
"We show that when the INM property holds, the degeneracy in a solution
can be removed by perturbing the function F slightly, i.e., the index
of a degenerate solution is equal to the index of a nondegenerate
solution of a slightly perturbed variational inequality problem. We
further show that our definition of the index is equivalent to the
topological index of the normal map at the zero corresponding to
the solution," wrote S.V. Melkonyan and colleagues, Yerevan State
University (see also Physics).
The researchers concluded: "As an application of our index formula,
we provide a global index theorem for variational inequalities which
holds even when the solutions are degenerate."
Melkonyan and colleagues published the results of their research
in Physica B - Condensed Matter (On the low-frequency limit
of the Schonfeld pulse 1/f law. Physica B - Condensed Matter,
2008;403(12):2029-2035).
For additional information, contact S.V. Melkonyan, Yerevan State
University, Dept. of Physics Semicond & Microelect, 1 Alex Manoogian
St., Yerevan 0025, Armenia.
The publisher of the journal Physica B - Condensed Matter can be
contacted at: Elsevier Science BV, PO Box 211, 1000 AE Amsterdam,
Netherlands.
Science Letter
July 15, 2008
According to a study from Yerevan, Armenia, "We provide an index
formula for solutions of variational inequality problems defined by a
continuously differentiable function F over a convex set At represented
by a finite number of inequality constraints. Our index formula can
be applied when the solutions are nonsingular and possibly degenerate,
as long as they also satisfy the injective normal map (INM) property,
which is implied by strong stability."
"We show that when the INM property holds, the degeneracy in a solution
can be removed by perturbing the function F slightly, i.e., the index
of a degenerate solution is equal to the index of a nondegenerate
solution of a slightly perturbed variational inequality problem. We
further show that our definition of the index is equivalent to the
topological index of the normal map at the zero corresponding to
the solution," wrote S.V. Melkonyan and colleagues, Yerevan State
University (see also Physics).
The researchers concluded: "As an application of our index formula,
we provide a global index theorem for variational inequalities which
holds even when the solutions are degenerate."
Melkonyan and colleagues published the results of their research
in Physica B - Condensed Matter (On the low-frequency limit
of the Schonfeld pulse 1/f law. Physica B - Condensed Matter,
2008;403(12):2029-2035).
For additional information, contact S.V. Melkonyan, Yerevan State
University, Dept. of Physics Semicond & Microelect, 1 Alex Manoogian
St., Yerevan 0025, Armenia.
The publisher of the journal Physica B - Condensed Matter can be
contacted at: Elsevier Science BV, PO Box 211, 1000 AE Amsterdam,
Netherlands.