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Papers by Thiên Huỳnh Công
Journal of Elasticity, 1979
In this paper the representation of displacement fields in linear elasticity in terms of harmonic... more In this paper the representation of displacement fields in linear elasticity in terms of harmonic functions is considered. In the original work of Papkovich and Neuber four harmonic functions were presented with a subsequent reduction to three on the grounds that only three are sufficient for the representation of displacements fields. This reduction is unsubstantiated and several authors have investigated
Discrete Mathematics, 1982
A one-dimensional random walk with unequa.1 step lengths restricted by tin absorbing barrier is c... more A one-dimensional random walk with unequa.1 step lengths restricted by tin absorbing barrier is considered as follows: (1) ezmmeration of the number of non-decreasing paths in a non-negative quadrant of the integral square lattice and in the inside of a polygon, (2) evaluatiion of trarlsient (or absorption) probabilities for tbe random wblk.
Discrete Mathematics, 1983
We deal with non-decreasing paths on the non-negative quadrant of the integral square lattice, ca... more We deal with non-decreasing paths on the non-negative quadrant of the integral square lattice, called by minimal lattice paths, from (0,O) to a point (n, m) restricted by two parallel lines with an incline k (20). We express the generating functions of the number of these distinct minimal lattice paths in terms of the polynomials (-x)', n ao. Formulas obtained thus include the generating function of the so-called higher Catalan number Ck(n) or Ballot numbers as the Special case. The number of minimal lattice paths for k = 1 is given as an explicit form by expanding the corresponding generating function.
Journal of Elasticity, 1979
In this paper the representation of displacement fields in linear elasticity in terms of harmonic... more In this paper the representation of displacement fields in linear elasticity in terms of harmonic functions is considered. In the original work of Papkovich and Neuber four harmonic functions were presented with a subsequent reduction to three on the grounds that only three are sufficient for the representation of displacements fields. This reduction is unsubstantiated and several authors have investigated
Discrete Mathematics, 1982
A one-dimensional random walk with unequa.1 step lengths restricted by tin absorbing barrier is c... more A one-dimensional random walk with unequa.1 step lengths restricted by tin absorbing barrier is considered as follows: (1) ezmmeration of the number of non-decreasing paths in a non-negative quadrant of the integral square lattice and in the inside of a polygon, (2) evaluatiion of trarlsient (or absorption) probabilities for tbe random wblk.
Discrete Mathematics, 1983
We deal with non-decreasing paths on the non-negative quadrant of the integral square lattice, ca... more We deal with non-decreasing paths on the non-negative quadrant of the integral square lattice, called by minimal lattice paths, from (0,O) to a point (n, m) restricted by two parallel lines with an incline k (20). We express the generating functions of the number of these distinct minimal lattice paths in terms of the polynomials (-x)', n ao. Formulas obtained thus include the generating function of the so-called higher Catalan number Ck(n) or Ballot numbers as the Special case. The number of minimal lattice paths for k = 1 is given as an explicit form by expanding the corresponding generating function.