We give a combinatorial interpretation for the super Catalan number S(m,m + s) for s ≤ 3 using lattice paths and make an attempt at a combinatorial interpretation for s = 4. We also examine the integrality of some factorial ratios.

The effect of the Transcendental Meditation (TM) technique on working memory and field independence was investigated in a twelve-week longitudinal time-series study in which the uMatch Me" computerized memory game and the Rod and Frame Test were administered daily to a matched pair of 11-year-old boys and a matched pair of 14-year-old girls. One of the boys and one of the girls began the TM tec...

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the objective of this work was to develop bioadhesive topical gel of aceclofenac with the help of response-surface approach. experiments were performed according to a 3-level factorial design to evaluate the effects of two independent variables [amount of poloxamer 407 (pl-407 = x1) and hydroxypropylmethyl cellulose k100 m (hpmc = x2)] on the bioadhesive character of gel, rheological property o...

A diallel cross is a set of all possible matings between several genotypes, which may be individuals, clones, homozygous lines, etc. Such crosses are used to estimate general and specific combining abilities of lines and crosses respectively. For ‘n’ inbreed lines, the possible F1’s are n(n–1)/2, which are to be tested in a suitably replicated randomized design. With facilities available for te...

BACKGROUND The 2 × 2 factorial design is widely used for assessing the existence of interaction and the extent of generalizability of two factors where each factor had only two levels. Accordingly, research problems associated with the main effects and interaction effects can be analyzed with the selected linear contrasts. METHODS To correct for the potential heterogeneity of variance structu...

A novel, supersaturable self-microemulsifying drug delivery system (S-SMEDDS) was successfully formulated to enhance the dissolution and oral absorption of valsartan (VST), a poorly water-soluble drug, while reducing the total quantity for administration. Poloxamer 407 is a selectable, supersaturating agent for VST-containing SMEDDS composed of 10% Capmul® MCM, 45% Tween® 20, and 45% Transcutol...

Blocked designs are useful in experiments. The general minimum lower order confounding (GMC) is an elaborate criterion which was proposed for selecting optimal fractional factorial designs. Zhang and Mukerjee (2009b) extended the GMC criterion to the B-GMC criterion for selecting a 2n−m : 2r design, where 2n−m : 2r denotes a two-level regular blocked design withN = 2n−m runs, n treatment factor...

Sequential experiment design strategies have been proposed for efficiently augmenting initial designs to solve many problems of interest to computer experimenters, including optimization, contour and threshold estimation, and global prediction. We focus on batch sequential design strategies for achieving maturity in global prediction of discrepancy inferred from computer model calibration. Pred...