This paper traces how in Britain and Germany, for-profit non-profit businesses coevolved with political-economic institutions. Starting the late eighteenth century, embraced logic of liberal capitalism, although path was not smooth. Over same period, German states balanced both social-welfare ideals. Social-welfare ideals did gain support until start twentieth century. The market embodied by mo...

This paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

The objective of this paper is to introduce the fundamental algebro-geometric constructions over the extended tropical semi-ring. The study of tropical varieties, co-varieties and ideals over this extension eventually yields the theorem of the weak tropical Nullstellensatz and gives an algebraic interpretation of the tropical Nullstellensatz.

A family of 2א0 Borel ideals on a compact lattice are constructed such that no two quotient lattices by ideals from this family are isomorphic.

Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping   from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two m...

Assume we are given a K -trivially invariant line e. The goal of the present article is to classify co-bijective algebras. We show that every natural, negative, semi-Eratosthenes monoid is stable. In this context, the results of [31] are highly relevant. In [31], the authors extended reducible ideals.

Mond-Weir type duals for multiobjective variational problems are formulated. Under generalized vector variational type I invexity assumptions on the functions involved, sufficient optimality conditions, weak and strong duality theorems are proved efficient and properly efficient solutions of the primal and dual problems.

Subgradient methods for SVMs have been successful in solving the primal formulation with linear kernels. The approach is extended here to nonlinear kernels, and the assumption of strong convexity of the objective is dropped, allowing an intercept term to be used in the classifier.

A multiobjective nonlinear programming problem is considered. Sufficiency theorems are derived for efficient and properly efficient solutions under generalized (F, ρ)-convexity assumptions. Weak, strong and strict converse duality theorems are established for a general Mond–Weir type dual relating properly efficient solutions of the primal and dual problems.

We consider nonsmooth multiobjective fractional programming problems with inequality and equality constraints. We establish the necessary and sufficient optimality conditions under various generalized invexity assumptions. In addition, we formulate a mixed dual problem corresponding to primal problem, and discuss weak, strong and strict converse duality theorems.