In the present note a MAPLE subroutine computing Milnor and Tyurina numbers of an isolated algebraic hypersurface singularity is presented and described in detail.

This article describes the subroutine library SLICOT that provides Fortran 77 implementations of numerical algorithms for computations in systems and control theory. Around a nucleus of basic numerical linear algebra subroutines, this library builds methods for the design and analysis of linear control systems. A brief history of the library is given together with a description of the current v...

and Applied Analysis 3 Proof. Since f(x) defined in (2) belongs to the PDGstructured family and by Lemma 2.1 in [16] the Clarke subdifferential of F(x, ρ) at x can be formulated by ∂F (x, ρ) = ∂f (x) + ρ∂G (x) = ∂f (x) + ρ conv { ∇g j (x) | j ∈ J (x) ∪ {0}}

The paper aims at investigating the effects of chemical reaction and thermal radiation on the steady two-dimensional laminar flow of viscous incompressible electrically conducting micropolar fluid past a stretching surface embedded in a non-Darcian porous medium. The radiative heat flux is assumed to follow Rosseland approximation. The governing equations of momentum, angular momentum, energy, ...

The present paper proposes a mathematical development of the plasticity and damage approaches to simulate sheet metal forming processes. It focuses on numerical prediction deformation during deep drawing process when crack appears. Anisotropic constitutive equations are proposed. A fully implicit integration coupling is used leads two nonlinear local scalar that solved by Newton’s method. devel...

Hoffman and Schwartz [13] developed the Lattice Polyhedron model and proved that it is totally dual integral (TDI), and so has integral optimal solutions. The model generalizes many important combinatorial optimization problems such as polymatroid intersection, cut covering polyhedra, min cost aborescences, etc., but has lacked a combinatorial algorithm. The problem can be seen as the blocking ...

Automated deduction techniques are being used in a system called Amphion to derive, from graphical speci cations, programs composed from a subroutine library. The system has been applied to construct software for the planning and analysis of interplanetary missions. The library for that application is a collection of subroutines written in FORTRAN-77 at JPL to perform computations in solar-syst...

This paper positively solves the quantum subroutine problem for fully quantum oracles. The quantum subroutine problem asks whether a quantum computer with an efficiently computable oracle can be efficiently simulated by a non-oracle quantum computer. We extends the earlier results obtained by Bennett, Bernstein, Brassard, and Vazirani, and by Aharonov, Kitaev, and Nisan to the case where the or...