Forced hydraulic jump in a horizontal stilling basin with one and two continuous sills at the downstream end of an ogee standard weir was investigated. Experiments were completed on sills of five different heights which were fixed at two different distances from the toe of the weir. The main characteristics of the jump such as the sequent depth ratio, relative roller length, and relative ener...

ANSYS-CFX is an effective and multipurpose software which can be used for simulation the computational fluid dynamics (CFD) solutions at all levels of complexity. This software can be used for numerical solution of two and three dimensional flows, compressible and incompressible flows, viscous and non-viscous flows, laminar and turbulent flows, Newtonian and non-Newtonian flows, porous media, s...

Convexity assumptions for fractional programming of variational type are relaxed to generalized invexity. The sufficient optimality conditions are employed to construct a mixed dual programming problem. It will involve the Wolfe type dual and Mond-Weir type dual as its special situations. Several duality theorems concerning weak, strong, and strict converse duality under the framework in mixed ...

The method of maximum likelihood (ML), introduced by Fisher (1921), is widely used in human and quantitative genetics and we draw upon this approach throughout the book, especially in Chapters 13–16 (mixture distributions) and 26–27 (variance component estimation). Weir (1996) gives a useful introduction with genetic applications, while Kendall and Stuart (1979) and Edwards (1992) provide more ...

In a recent volume chronicling the historical evolution of assessment constructs and the way these are operationalised through language tests, Weir (2013b) noted how for much of the 20th century the teaching and testing of reading focused on lower-level processing to extract factual meaning at the clause and sentence level, rather than on higher-level processing to combine and integrate textbas...

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.

A new notion of higher-order weakly generalized adjacent epiderivative for a set-valued map is introduced. By virtue of the epiderivative and weak minimality, a higher-order Mond-Weir type dual problem and a higher-order Wolfe type dual problem are introduced for a constrained setvalued optimization problem, respectively. Then, corresponding weak duality, strong duality and converse duality the...

A class of second order (F,a,q,d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond–Weir type multiobtive dual. 2005 Elsevier Inc. All rights reserved.

In this paper, new classes of generalized (F,α,ρ, d)-V -type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.

We show that the class of level-k control languages, as defined by Weir, is properly included in the class of 2k−1-multiple context-free languages for each k ≥ 2. The proof of inclusion uses a representation of the set of derivation trees for a level-k control language in terms of a second-order abstract categorial grammar.