In this study, we define unrestricted Pell and – Lucas hyper-complex numbers. We choose arbitrary numbers for the coefficients of ordered basis 〖{e〗_0,e_1,⋯,e_(N-1)} 2^N-ons where N∈{0,1,2,3,4} call these Pell-Lucas 2N-ons. give generating functions Binet formulas type also obtain some generalization well known identities such as Catalan’s, Cassini’s d’Ocagne’s identities.

Disease-related malnutrition is common, detrimentally affecting the patient and healthcare economy. Although use of high protein oral nutritional supplements (ONS) has been recommended to counteract the catabolic effects of disease and to facilitate recovery from illness, there is a lack of systematically obtained evidence to support these recommendations. This systematic review involving 36 ra...

BACKGROUND There is no consensus on the type, time of initiation, or duration of use of enteral nutrition in patients with chronic kidney disease (CKD). This study aimed to compare the effects of a renal-specific oral nutrition supplement (RS-ONS) and a standard recommended nutrition regime on biochemical and nutrition markers in malnourished patients with CKD on hemodialysis. METHODS Sixty-t...