The following propositions are true: (1) For all real numbers r, s such that 0 ≤ r and s · s < r · r holds s < r. (2) For all real numbers r, s such that 1 < r and r · r ≤ s holds r < s. (3) For all natural numbers a, n such that a > 1 holds an > n. (4) For all natural numbers n, k, m such that k ≤ n and m = b n2 c holds (n m ) ≥ (n k ) . (5) For all natural numbers n, m such that m = b n2 c an...

In this paper, we discuss the properties of the hyperfibonacci numbers F [r] n and hyperlucas numbers L [r] n . We investigate the log-concavity (log-convexity) of hyperfibonacci numbers and hyperlucas numbers. For example, we prove that {F [r] n }n≥1 is log-concave. In addition, we also study the log-concavity (log-convexity) of generalized hyperfibonacci numbers and hyperlucas numbers.

in order to evaluate phenological characteristics, yield and yield components of 18 cold tolerant lentil genotypes in fall planting under supplementary irrigation, an experiment was carried out based on randomized complete block design in 2006-2007 at research farm of college of agriculture, ferdowsi university of mashhad. irrigation was performed three times: immediately after sowing, 20 days ...

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.

aims: air is the combination of atmospheric components or physical conditions of the current atmosphere in a certain place and a certain time. the aim of this study was to assess the relationship between weather components, air atmospheric pollutants and the number of individuals that were hospitalized due to cardiovascular diseases in polluted days. instrument & methods: in this descriptive st...