We show that there are universal positive constants c and C such the mixing time τmix for the fifteen puzzle in an n× n torus satisfies cn logn ≤ τmix ≤ Cn log n.

The objective of this study was to determine the effects of mixing time (mixer efficiency) of diets containing several low-inclusion ingredients (crystalline AA, ZnO, a medication, and vitamin and trace mineral premixes) on growth performance of nursery pigs. In a pilot study, mixing efficiency of a 1,360-kg capacity, horizontal ribbon mixer was evaluated with salt of different particle sizes (...

Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetr...

The eigenvalue or spectral gap of a Markov chain is the difference between the two largest eigenvalues of the transition matrix of its underlying (state space) graph. In this paper we explore the intimate relationship between the spectral gap of a Markov chain and its mixing time, as well as another closely related structural property of a Markov chain known as conductance. The relationships am...

objective: previous studies have demonstrated that dental stone casts can be disinfected by replacing 10v% of required water with 5.25% sodium hypochlorite solution. this comparative study evaluated physical properties of dental stone models produced by replacing distilled water with sodium hypochlorite.   methods: in this in-vitro experimental study, a total of 45 dental stone models were prod...

We show that the mixing time for the fifteen puzzle in an n× n torus is on the order of n logn.

Consider a deck of n cards. Let p1, p2, . . . , pn be a probability vector and consider the mixing time of the card shuffle which at each step of time picks a position according to the pi’s and move the card in that position to the top. This setup was introduced in [5], where a few special cases were studied. In particular the case pn−k = pn = 1/2, k = Θ(n), turned out to be challenging and onl...

introduction: this study aimed to compare the cytotoxicity of mta fillapex, ah-26 and apatite root canal sealers at different times after mixing. methods and materials: in this in vitro study, mta fillapex, ah-26 and apatite root canal sealer were spilled uniformly by 40 µm mesh in a 96-well plate. then, human fetal foreskin fibroblast cell line (hfff2) were added to each sealer cell culture me...

Making use of concrete materials in cut-off walls, because of their low permeability and standing high Hydraulic Gradient caused by underground drainage, has attracted great amount of attention. Using ordinary concrete with high elasticity modulus, compared to other materials may accompany with problems including brittleness of cutoffs due to dynamic stresses. To solve this problem, adding a ce...

Landfills generate leachate that contains elevated concentration of contaminants and is hazardous to human health and the ecosystem. In this study, the mixture of granular activated carbon and cockle shells was investigated for remediation of COD and ammonia from stabilized landfill leachate. All adsorbent media were sieved to a particle size between 2.00 and 3.35 mm. The optimum mixing ratio, ...