It has been consistently demonstrated that human proximal limb elements exhibit negative allometry, while distal elements scale with positive allometry. Such scaling implies that longer limbs will have higher intralimb indices, a phenomenon not borne out by empirical analyses. This, therefore, creates a paradox within the limb allometry literature. This study shows that these apparently conflic...

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.

We consider T f = ∫ x1 0 ∫ x2 0 f (t1, t2)dt1dt2 and a corresponding geometric mean operator G f = exp(1/x1x2) ∫ x1 0 ∫ x2 0 log f (t1, t2)dt1dt2. E. T. Sawyer showed that the Hardy-type inequality ‖T f ‖Lq u ≤ C‖ f ‖Lp v could be characterized by three independent conditions on the weights. We give a simple proof of the fact that if the weight v is of product type, then in fact only one condit...

some physical properties and chemical compositions of two cultivars (semsouri and shahabadi) of cantaloupe studied during four different stages of maturity from fruit set to completely ripe. the physical properties investigated were the geometric mean diameter (gmd), specific gravity (sg), mean firmness (mf), rind, seed (%) and flesh (%). the chemical compositions were brix, titrable acidity (t...

Let Ai and Bi be positive definite matrices for all i=1,…,m. It is shown that|||∑i=1m(Ai2♯Bi2)r|||≤|||((∑i=1mAi)rp2(∑i=1mBi)rp(∑i=1mAi)rp2)1p|||, unitarily invariant norms, where p>0 r≥1 such that rp≥1. This gives an affirmative answer to a conjecture posed by Dinh, Ahsani Tam. The preceding inequality directly leads recent result of Audenaert in 2015.