‎in this paper, using the idea of convexificators, we study boundedness and nonemptiness of lagrange multipliers satisfying the first order necessary conditions. we consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. within this context, define generalized mangasarian-fromovitz constraint qualification and show t...

Corrected Miller–Tucker–Zemlin type subtour elimination constraints for the capacitated vehicle routing problem are presented. 2003 Elsevier B.V. All rights reserved.

1 The " convex " KKT theorem: a recapitulation We recall the Karush-Kuhn-Tucker theorem for convex programming, as treated in the previous lecture (see Corollary 3.5 of [OSC]).

Recently, Gross, Mansour and Tucker introduced the partial-twuality polynomials. In this paper, we find that when there are enough parallel edges, any multiple graph is a negative answer to problem 8.7 in their paper (Gross et al., 2021): Is restricted-orientable partial-Petrial polynomial of an arbitrary ribbon even-interpolating? addition, also counterexample conjecture 8.1 Tucker: If partial...

Extended Thermodynamics of dense gases is characterized by two hierarchies of field equations, which allow one to overcome some restrictions on the generality of the previous models. This idea has been introduced by Arima, Taniguchi, Ruggeri and Sugiyama. In the case of a 14-moment model, they have found the closure of the balance equations up to second order with respect to equilibrium. Here, ...

Partial duality is a of ribbon graphs relative to subset their edges generalizing the classical Euler–Poincaré duality. This operation often changes genus. Recently J.L. Gross, T. Mansour, and T.W. Tucker formulated conjecture that for any graph different from plane trees partial duals, there which does change A family counterexamples was found by Qi Yan Xian’an Jin. In this note we prove essen...

Throughout the world, elections are being used in increasing numbers of nations. Conducting elections is seen as providing legitimacy to elected leaders, as long as they are conducted fairly and with integrity. But it also seems that along with the trends toward more elections around the world there are increasing concerns about electoral fraud and the potential manipulation of the electoral pr...