For a function f : {0, 1} → R and an invertible linear transformation L ∈ GLn(2), we consider the function Lf : {0, 1} → R defined by Lf(x) = f(Lx). We raise two conjectures: First, we conjecture that if f is Boolean and monotone then I(Lf) ≥ I(f), where I(f) is the total influence of f . Second, we conjecture that if both f and L(f) are monotone, then f = L(f) (up to a permutation of the coord...

Abstract. Let B+ ⊂ GLn(R) denote the subgroup of upper triangular n × nmatrices with positive entries on the main diagonal. A matrix M ∈ B+ is called totally positive if the determinants of all its minors not containing a row or column lying completely under the main diagonal are positive. We give a simple determinantal equation for the boundary of all positive upper triangular matrices in B+.

We prove a lower bound of 52n 2 3n for the rank of n n–matrix multiplication over an arbitrary field. Similar bounds hold for the rank of the multiplication in noncommutative division algebras and for the multiplication of upper triangular matrices.

For many decision problems with uncertainty, triangular intuitionistic fuzzy number is a useful tool in expressing ill-known quantities. This paper develops a novel decision method based on zero-sum game for multiple attribute decision making problems where the attribute values take the form of triangular intuitionistic fuzzy numbers and the attribute weights are unknown. First, a new value ind...

Bionanotechnology is a combination of three terms: “bios” meaning “life,” “nano” (origin in Greek) meaning “dwarf,” and “technologia” (origin in Greek—comprised of “techne” meaning “craft,” and “logia” meaning “saying”), which is a broad term dealing with the use and knowledge of humanity’s tools and crafts. Biomolecular Nanotechnology—or Bionanotechnology—is a term coined for the area of study...

Bulk quantities of polypyrrole nanofibers and nanospheres can be synthesized with a facile, one-step "green-nano" chemical oxidative polymerization approach, by simply using different reaction media.

In this article, we study dynamics of adsorbate island formation in a model plasma-condensate system numerically. We derive the generalized reaction-diffusion model for adsorptive multilayer system by taking into account anisotropy in transfer of adatoms between neighbor layers induced by electric field. It will be found that with an increase in the electric field strength, a structural transfo...

New and unknown electrocatalytic oxidation of water was found to occur on a nano-gold attached palladium electrode. Since the oxidation potential was negative enough to that of well-known normal oxidation of water to form O2, the direct use of water as a fuel, instead of alcohols, might be possible using the nano-gold/palladium electrode.

A simple and precise size measurement device of microparticles in liquid has been developed by using a narrow gap between a cylindrical lens and a flat glass wall, in which the distance of the gap is precisely determined by the diffraction Moiré pattern of irradiated light. Two different methods to transfer the particles toward the center line of the lens, a hydrodynamic flow mode and an electr...

This study investigates geometrical non-linear analysis of composite circular cylindrical shells under external pressure over part of their surfaces and also shells subjected to combined axial compression and triangular external pressure. Donnell non-linear shell theory along with first order shear deformation theory (FOSD) are adopted in the analysis. In the case of combined axial compression ...