The native mathematical language of trigonometry is combinatorial. Two interrelated combinatorial symmetric functions underlie trigonometry. We use their characteristics to derive identities for the trigonometric functions of multiple distinct angles. When applied to the sum of an infinite number of infinitesimal angles, these identities lead to the power series expansions of the trigonometric ...

The most distinctive feature of this clearly written and engaging book is that throughout its ten chapters, the author simultaneously develops two independent projects. The first project, as the title suggests, is to introduce the novice to some of the traditional issues in the philosophy of mind. To this end, the book is structured around discussions of dualism, physicalism, the problem of oth...

A left ideal of any C∗-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed, left ideals in C∗-algebras may be characterized as the class of such operator algebras, which happen also to be triple systems. Conversely, we show here and in a sequel to this paper, that operator algebras with r.c.a.i. should be studied in terms of a certain le...

The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor identities within the latter class. The approach makes use of three fundamental features. Firstly a new transformation which maps a subset of the family of ...

Political elites often discuss racial/ethnic outgroups in a critical light. I claim this discourse raises the salience of group identity while impugning its worth, thus inducing differential political reactions among high and low identifying group members. Specifically, high identifiers will engage in political efforts that restore their identity’s positive value by displaying ingroup favoritis...

Using Lie theory, Stefano Capparelli conjectured an interesting Rogers-Ramanujan type partition identity in his 1988 Rutgers Ph.D. thesis. The first proof was given by George Andrews, using combinatorial methods. Later, Capparelli was able to provide a Lie theoretic proof. Most combinatorial Rogers-Ramanujan type identities (e.g. the Göllnitz-Gordon identities, Gordon’s combinatorial generaliza...

and [0] = 1. Observe that this identity is valid in the ring of polynomials in z1, · · · , zm+1 over Z[q, q]. From combinatorial viewpoint the identity (1.1) is equivalent tom+2 identities of linear relations among Hall-Littlewood polynomials [6] associated to certain tuples (not necessary partitions). The first and the last of these linear relations are actually equivalent to the well-known q-...

theories of identity1 and to describe how various social contexts and cognitive motives influence the process of identity change. Although many strands of literature describe identity dynamics, two are considered primary: identity theory (Stryker 1980; Stryker and Serpe 1982) and social identity theory (Tajfel 1981; Tajfel and Turner 1986; Turner et al. 1987). Recent literature has tried to com...

A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...