We show that the free hyperplane arrangements form a Zariski-closed set in various parameter spaces. Given a geometric lattice L let V(L) be the parameter space of arrangements with intersection lattice isomorphic to L. Coupling our result with a theorem of Yuzvinsky, we conclude that in V(L) the free arrangements are parameterized by a union of connected components of V(L).

Succinct non-interactive arguments (SNARGs) enable verifying NP computations with substantially lower complexity than that required for classical NP verification. In this work, we first construct a lattice-based SNARG candidate with quasi-optimal succinctness (where the argument size is quasilinear in the security parameter). Further extension of our methods yields the first SNARG (from any ass...

The experimental observation of a spin-gap in the antiferromagnetic spin2 compound CaV4O9 has been attributed to the formation of a plaquette resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace o...

Ni and Cu elemental powder mixtures containing 25, 50, and 75% at Cu were subjected to mechanical alloying in a planetary ball mill under various milling times. Structural evolution was analyzed by means of X-ray diffraction and scanning electron microscopy. Experimental results indicated that nanostructured solid solution alloy powders having homogeneous distribution of Ni and Cu were formed b...

The mechanical alloying process was used to synthesize the Ni50Al50−xMox nanocrystalline intermetallic compound using pure Ni and Al elemental powder. This process was carried out in the presence of various Mo contents as a micro-alloying element for various milling times. Structural changes of powder particles during mechanical alloying were studied by X-ray diffractometry (XRD) and scanning e...

A Synthesis of doped ceria by combustion method is performed. Two types of fuel such asurea and glycine is used to investigate the effect of fuel reactivity and reaction rate on themorphology of the resulted powders. Thermo gravimetric analysis is carried out by (TG/DTA,Rigaku Thermalplus TG 8120) to study the exo–endo temperature of as-received powder. Thecrystalline phases are identified by X...

In the present study, nanocrystalline Ni50Al50-xMox (X = 0, 0.5, 1, 2.5, 5) intermetallic compound was produced through mechanical alloying of nickel, aluminum, and molybdenum powders. AlNi compounds with good and attractive properties such as high melting point, high strength to weight ratio and high corrosion resistance especially at high temperatures have attracted the attention of many rese...

In this research nickel zinc ferrite nanoparticles with composition of Ni1-xZnxFe2O4 (where x=0, 0.3, 0.7, 1) were synthesized by a sol-gel method at 600 °C for 5 hours. The structure of nanoparticles was studied using X-ray diffraction pattern. The lattice parameter of ferrite nanoparticles was calculated and indicates lattice constant of nanoparticl...

Abstract There are various methods to produce iron based nano crystalline magnetic alloys. Among these methods, mechanical alloying is one of the most important. In this research, nano crystalline Fe85Si10Ni5 soft magnetic alloy was synthesized by mechanical alloying. The effect of alloying time on phase constituents and magnetic properties of the produced powders was investigated, by X-ray di...

In this research, calcium titanate nanoparticles have been synthesized via mechanical alloying (MA). By changing the parameters of mechanical alloying, optimal conditions for synthesis of this compound was determined. For synthesis of this compound, a mixture of calcium hydroxide and titanium dioxide, rotation speed of 250 rpm and differnet ball to powder weight ratio was used. Phase investigat...