In this paper, we present a new lower bound on the size of separating hash families of type {wq−1 1 , w2} where w1 < w2. Our result extends the paper by Guo, Stinson and Tran on binary frameproof codes [Des. Codes Crypto. 77 (2015), 301–319]. This bound compares well against known general bounds, and is especially useful when trying to bound the size of strong separating hash families. We also ...

Let cn = 1 n + 1 ( 2n n ) be the nth Catalan number. In this paper, we look at some of the arithmetic properties of cn. For example, we show that w2(cn) ! log log n for all n ! 3 provided that cn is odd, where w2(m) is the Hamming weight (or the binary sum of digits) of the positive integer m. We also determine all instances in which cn is a base 2 palindrome, and prove that the first k odd Cat...

Throughout, w, Γ, and∧ denote the classes of all, entire, and analytic scalar-valued single sequences, respectively. We write w2 for the set of all complex sequences (xmn), where m,n ∈ N is the set of positive integers. Then, w2 is a linear space under the coordinatewise addition and scalar multiplication. Some initial works on double sequence spaces are found in Bromwich [1]. Later on, they we...

By δ and wk denote the minimum degree and minimum degree-sum (weight) of a k-vertex path in a given graph, respectively. For every 3-polytope, w2 6 13 (Kotzig, 1955) and w3 6 21 (Ando, Iwasaki, Kaneko, 1993), where both bounds are sharp. For every 3-polytope with δ > 4, we have sharp bounds w2 6 11 (Lebesgue, 1940) and w3 6 17 (Borodin, 1997). Madaras (2000) proved that every triangulated 3-pol...

Wheat (Triticum aestivum L.) seedling establishment is very sensitive to temperature and drought stresses. The present study was conducted investigate the effects of foliar exogenous 5-aminolevulinic acid (5-ALA) application on wheat under different (25, 30, 35 ℃) water regimes (normal 65% watering). Five levels 5-ALA (0, 25, 50, 100 150 mg L-1) were applied as application. Leaf area, stem di...

Background The COVID-19 pandemic and the policies to contain it had a widespread impact on life livelihood of participants enrolled in Srinivaspura Aging, Neuro Senescence, COGnition (SANSCOG) study. We evaluated prevalence depression associated with its cognition our cohort. Method used geriatric scale (GDS) objectively assess scores 400 before first wave (March 2020; W1) after second 2021; W2...

The total atomization energy at absolute zero, (TAE0) of benzene, C6H6, was computed fully ab initio by means of W2h theory as 1306.6 kcal/mol, to be compared with the experimentally derived value 1305.7±0.7 kcal/mol. The computed result includes contributions from inner-shell correlation (7.1 kcal/mol), scalar relativistic effects (-1.0 kcal/mol), atomic spin-orbit splitting (-0.5 kcal/mol), a...