Physicochemical properties of pork patties formulated with black rice powder were investigated. Moisture contents of samples containing black rice powder were significantly higher than that of the control (p<0.05). Protein, fat, and ash contents increased with increasing black rice powder content. Uncooked and cooked pH values of samples increased with increasing black rice powder content. Ligh...

The objective of the present study is to investigate the effects of irrigation water salinity,cow manure levels and different planting methods on ions variation in soil and their uptake bysaffron. A split-split plot arrangement was conducted in a randomized complete block designwith irrigation water salinity levels (0.45 (fresh water, S1), 1.0 (S2), 2.0 (S3) and 3.0 (S4) dS m-1)as the main plot...

We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we show that the 2n-th moment of the trace of a random k-dimensional unitary matrix is equal to the number of permutations of length n with no increasing subsequence of length greater than k. We then generalize this to ot...

Let 〈a1, a2, . . . , an〉 be a sequence of comparable elements. In this paper, we study two constrained versions of the longest increasing subsequence (LIS) problem. The first problem is the range-constrained longest increasing subsequence (RLIS) problem. Given 0 < LI ≤ UI < n and 0 ≤ LV ≤ UV , the objective of the RLIS problem is to deliver a maximum-length increasing subsequence 〈ai1 , ai2 , ....

The number of even 321-avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 2 th Catalan number otherwise. We present an involution that proves a refinement of this sign-balance property respecting the length of the longest increasing subsequence of the permutation. In addition, this yields a combinatorial proof of a recent analogous resul...