We consider linear programming (continuous or integer) where some matrix entries are decision parameters. If the variables are nonnegative the problem can be easily solved in two phases. It is shown that direct costs on the matrix entries make the problem NP-hard. Finally a strong duality result is provided.

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...

This paper introduces an inequality on vectors in $mathbb{R}^n$ which compares vectors in $mathbb{R}^n$ based on the $p$-norm of their projections on $mathbb{R}^k$ ($kleq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $sum_{i=1}^kvert x_ivert^p$ is less than or equal to $ sum_{i=1}^kvert y_ivert^p$, for every $dleq kleq n$. For...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

In this paper, we consider a number of technical problems associated with identification of linear systems using quantized and intermittent information. More specifically, we study asymptotic properties for identification of such systems, including strong consistency, asymptotic normality and asymptotic efficiency, and determine their relationship with quantization errors and the packet losses....

Background and Objective:Outbreak of food-borne diseases has become more and more important these days and using natural food preservers with high durability is under debate. Vegetative essence is a type of food preserver and many studies have been performed on their antimicrobial effects. The purpose of this study was to investigate antibacterial effects of lavender essence on...

Strong normalization for linear logic requires elaborated rewriting techniques. In this paper we give a new presentation of MELL proof nets, without any commutative cut-elimination rule. We show how this feature induces a compact and simple proof of strong normalization, via reducibility candidates. It is the first proof of strong normalization for MELL which does not rely on any form of conflu...