Mentoring programs show promise for preventing emotional and behavioral problems among at-risk youth, but little is known about processes that may be most critical to achieving this end. This study explored indicators of positive youth development (PYD; competence, confidence, connection, care and compassion, character)

We introduce and study in detail an invariant of (1, 1) tangles. This invariant, derived from a family of four dimensional representations of the quantum superalgebra U q [gl(2|1)], will be referred to as the Links-Gould invariant. We find that our invariant is distinct from the Jones, HOMFLY and Kauffman polynomials (detecting chirality of some links where these invariants fail), and that it does not distinguish mutants or inverses. The method of evaluation is based on an abstract tensor state model for the invariant that is quite useful for computation as well as theoretical exploration.

The anodic behavior of zinc in strongly alkaline solutions was studied making special note of the limiting current density and of the overvoltage for the zinc/zincate reaction. The effect of temperature, KOH concentration, presence of zincate, and amalgamation on these values was measured. Under the conditions studied, zincate ion diffusion away from the electrode controls the limiting current density. The overvoltage at amalgamated electrodes is that for the charge transfer reaction, while at nonamalgamated electrodes it is due to adatom diffusion.In developing and designing alkaline batteries using zinc anodes, there are several modifications that can be made to improve the performance of the system. One such modification is the amalgamation of the zinc electrode. This is done in practically all zinc-alkaline batteries. The purpose is to raise the hydrogen overvoltage and thus reduce the corrosion or open-circuit reaction. This amalgamation, however, may also affect the other zinc electrode processes.A review of the published literature revealed that few factual data are available to show what effect electrolyte concentration, amalgamation, zincate concentration, and temperature have on the anodic processes of the zinc/zincate electrode. For this reason a program of work was undertaken to obtain such information, and the results are reported here.

It is known that the first two-variable Links-Gould quantum link invariant LG ≡ LG 2,1 is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations of LG for prime knots. Through them, we show that the invariant is complete, modulo mutation, for all prime knots (including reflections) of up to 11 crossings, but fails to distinguish some nonmutant pairs of 12-crossing prime knots. As a byproduct, we classify the mutants within the prime knots of 11 and 12 crossings. In parallel, we learn thatLG distinguishes the chirality of all chiral prime knots of at most 12 crossings. We then demonstrate that every mutation-insensitive link invariant fails to distinguish the chirality of a number of 14-crossing prime knots. This provides 14-crossing examples of chiral prime knots whose chirality is undistinguished by LG. The Links-Gould invariantFor any positive integers m and n, the Links-Gould quantum link invariant LG m,n is a two-variable invariant of oriented links. We here describe it using the variables q and p ≡ q α+(m−n)/2 which are inherited from its definition via the 2 mn -dimensional α-parametric representation of highest weight (0 m |α n ) of the quantum superalgebra U q [gl(m|n)]. Its construction was originally described in [12,25], and some of its properties together with some concrete evaluations are available in [5,6,8,9].The case LG 1,1 , in which the two variables degenerate to a single variable (p), is actually the Alexander-Conway polynomial, and the next simplest case, LG 2,1 , is the first truly two-variable invariant of the family. Apart from LG 1,1 , more is known about LG 2,1 than about any of its kin [4,[15][16][17][18][19][20][21], and we generally refer to LG 2,1 as the Links-Gould invariant LG. In particular, it has been proven to be polynomial [17]; this is still only surmised for general LG m,n .

We show that the Alexander-Conway polynomial ∆ is obtainable via a particular one-variable reduction of each two-variable Links-Gould invariant LG m,1 , where m is a positive integer. Thus there exist infinitely many two-variable generalisations of ∆. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG m,1 does not satisfy a second-order characteristic identity unless m = 1. To demonstrate that the one-variable reduction of LG m,1 satisfies the defining skein relation of ∆, we evaluate the kernel of a quantum trace.