The Minimum Rank Problem: a counterexample

We provide a counterexample to a recent conjecture that the minimum rank of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a consequence of the counterexample, we show that there is a graph for which the minimum rank over the reals is strictly smaller than the minimum rank over the rationals. We also make some comments on the minimum rank of sign pattern matrices over different subfields of $\mathbb R$.Comment: 4 pages, 1 figur

Wind and Solar Cell-Based Distribution System for Different Load Variations Using Fuzzy Logic Controller

The proposed system presents power-control strategies of a grid-connected hybrid generation system with versatile power transfer. This hybrid system allows maximum utilization of freely available renewable energy sources like wind and photovoltaic energies . For this, an adaptive MPPT algorithm along with standard perturb and observe method will be used for the system.Also, this configuration allows the two sources to supply the load separately or simultaneously depending on the availability of the energy sources. The turbine rotor speed is the main determinant of mechanical output from wind energy and Solar cell operating voltage in the case of output power from solar energy. Permanent Magnet Synchronous Generator is coupled with wind turbine for attaining wind energy conversion system . The inverter converts the DC output from non-conventional energy into useful AC power for the connected load . This hybrid system operates under normal conditions which include normal room temperature in the case of solar energy and normal wind speed at plain area in the case of wind energy. A fuzzy based PWM system will be designed to reduce the harmonic ripples. The simulation results are presented to illustrate  the operating principle, feasibility and reliability of this proposed system. Keywords: smart grid, solar cell, fuzzy logic controlle

Geometry of good sets in n-fold Cartesian product

We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.Comment: 17 pages, no figures, no table

Art in Internal Ballistics

A review of the computations in Internal Ballistic Systems for developing pressure and velocity space curves, called primary problem and differential variations due to change in initial phase space of loading conditions, called secondary problem, is presented. In the concluding part, the general aspects of the secondary problem are analysed and reported

The character of non-manipulable collective choices between two alternatives

We consider classes of non-manipulable two-valued social choice functions, i.e., social choice functions with range of cardinality two within a larger set of alternatives. Corresponding to the different classes, the functional forms are described. Further we show that they, and some others from previous literature, can all be unified using a common structure. Such a structure relies on the concept of character function we introduce. This is a function from the domain of the admissible profiles, that notably we do not assume to be universal, to a partially ordered set. The proper choice of the character function, marks the distinction among different classes and permits the description of all social choice functions of a class in simple terms.Comment: JEL Code: D7