In this paper, a new algorithm of approximating rational triangular B-B surfaces using polynomial triangular B-B surfaces is presented. This algorithm has a simple expression and insured convergence. The core idea of the algorithm is to yield a polynomial triangular B-B surface, which has the same degree and new control vertices of the degree-elevated rational triangular B-B surface, to approxi...

Consider a sum P N 1 Y i of random variables conditioned on a given value of the sum P N 1 X i of some other variables, where X i and Y i are dependent but the pairs (X i ; Y i) form an i.i.d. sequence. We prove, for a triangular array (X ni ; Y ni) of such pairs satisfying certain conditions, both convergence of the distribution of the conditioned sum (after suitable normalization) to a normal...

Continuous probability distributions are widely used to mathematically describe random phenomena in engineering and physical sciences. In this paper, we present a methodology that can be used to formalize any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Our methodology is primarily based on the Standard ...

Acyclic phase-type distributions are phase-type distributions with triangular matrix representations. They constitute a versatile modelling tool, since they (1) can serve as approximations to any continuous distributions, and (2) exhibit special properties and characteristics, which usually result in some ease in analysis. The size of the matrix representation has a strong influence on computat...

We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r ≥ 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor r equals to zero. We show that the possibility distribution of the IRR is a highly nonlinear function of quasi-trian...

We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This superexponential decay persists in lattices diluted to the rigidity percolation th...

A computationally intensive large job, granulized to concurrent pieces and operating in a dynamic environment should reduce the total processing time. However, distributing jobs across a networked environment is a tedious and difficult task. Job distribution in a Local Area Network based on Triangular Dynamic Architecture (TDA) is a mechanism that establishes a dynamic environment for job distr...

In this paper, we first review local counting methods for perimeter estimation of piecewise smooth binary figures on square, hexagonal, and triangular grids. We verify that better perimeter estimates, using local counting algorithms, can be obtained using hexagonal or triangular grids. We then compare surface area estimates using local counting techniques for binary three-dimensional volumes un...

We list several open problems concerning the enumeration of directed animals on two-dimensional lattices. We show that most of these problems are special cases of two central problems: calculating the position generating function and the perimeter and area generating function for square lattice animals. We propose a possible direction for solving these two problems: we extend Dhar's corresponde...

Triangular enclosures are typical configurations found in attic spaces of residential as well as industrial pitched-roof buildings. Previous studies on airflow within such spaces have focused on the laminar range. A numerical study has been carried out for time-dependent, two-dimensional low turbulence natural convection of air contained in the attic of a pitched roof of triangular crosssection...