A composition of an integer constrained to have decreasing then increasing parts is called concave. We prove that the generating function for the number of concave compositions, denoted v(q), is a mixed mock modular form in a more general sense than is typically used. We relate v(q) to generating functions studied in connection with “Moonshine of the Mathieu group” and the smallest parts of a p...

the study was carried out on 120 crossbred holstein × shahiwal dairy cows for a period of 150 days to quantify the influence of dietary energy and protein intake on yield and composition of milk. total 12 dairy farms having similar housing systems and holding at least 20 dairy cows in between mid to late lactation were selected for study purposes. the farms were located in the peri-urban and ur...

An integer composition of a nonnegative integer n is a tuple (π1, . . . , πk) of nonnegative integers whose sum is n; the πi’s are called the parts of the composition. For fixed number k of parts, the number of f -weighted integer compositions (also called f -colored integer compositions in the literature), in which each part size s may occur in f(s) different colors, is given by the extended b...

BACKGROUND Circulating FGF21 levels are commonly elevated in disease states. There is limited information regarding concentrations of circulating FGF21 in the absence of disease, as well as age-related differences in body composition that may contribute to FGF21 regulation across groups. OBJECTIVE The objectives of this study were to assess FGF21 levels across age groups (childhood to elder a...

Polyunsaturated fatty acids (PUFA), a lipid family comprised of omega-3 (n-3) and n-6 fatty acids, are a critical component of cellular membranes, and recent in vitro studies have found that antipsychotic medications up-regulate genes responsible for PUFA biosynthesis. To evaluate this effect in vivo, rats were treated with risperidone (1.5, 3, 6mg/kg/day), paliperidone (1.5, 3, 6mg/kg/day), ol...

We present results from a large suite of simulations of Saturn’s dense A and B rings using a new model of particle sticking in local simulations (Perrine, R.P., Richardson, D.C., Scheeres, D.J. [2011]. Icarus 212, 719– 735). In this model, colliding particles can be incorporated into or help fragment rigid aggregations on the basis of certain user-specified parameters that can represent van der...

One of the most arresting phenomena in the theory of pattern avoidance by permutations is the fact that the number of permutations of n letters that avoid a pattern π of 3 letters is independent of π. In this note we exhibit two generalizations of this fact, to ordered partitions, a.k.a. compositions, of an integer, and to permutations of multisets. It is remarkable that the conclusions are in ...

A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The number of summands is called the number of parts of the composition. A palindromic composition of n is a composition of n in which the summands are the same in the given or in reverse order. In this paper we study the generating function for the number of compositions (respectively, palindromic ...

one of the methods of the past scholars for better and faster learning of sciences has been the versification of scientific material. this type of poetry is called ta‘līmī (didactic) in technical terms. many scholarly manẓūmas (poetic compositions) on such sciences as jurisprudence, uṣūl (principles of jurisprudence), ethics, logics, philosophy, theology, rijāl (biographies of dignitaries), and...

1 Mathematical indices, formed by combining several primary measures, can help researchers summarize, interpret and display results from plant competition experiments. This essay compiles and discusses more than 50 indices that have been used in studies of plant competition. 2 Indices allow researchers to quantify and express several attributes of plant competition, including competition intens...