A topological invariant, analogous to the linking number as defined in knot theory, is defined for pairs of digital closed paths of Z3. This kind of invariant is very useful for proofs which involve homotopy classes of digital paths. Indeed, it can be used for example in order to state the connection between the tunnels in an object and the ones in its complement. Even if its definition is not ...

Abstract. We study difference sets with parameters (v, k, λ) = (ps(r2m − 1)/(r − 1), ps−1r2m−1, ps−2(r − 1)r2m−2), where r = (ps − 1)/(p − 1) and p is a prime. Examples for such difference sets are known from a construction of McFarland which works for m = 1 and all p, s. We will prove a structural theorem on difference sets with the above parameters; it will include the result, that under the ...

As a first step towards computing instanton-generated superpotentials in heterotic standard model vacua, we determine the Gromov-Witten invariants for a Calabi-Yau threefold with fundamental group π1(X) = Z3 × Z3. We find that the curves fall into homology classes in H2(X,Z) = Z⊕ (Z3 ⊕Z3). The unexpected appearance of the finite torsion subgroup in the homology group complicates our analysis. H...

Cadmium (Cd) is extremely toxic metal and reduces plant growth. Therefore, study was conducted to evaluate the effect of various Cd levels 0, 5, 20, 50 and 80 mg L on seed germination and seedling growth of four wheat cultivars (Sehar-06, Fareed-06, Inqlab-91, Chakwal-50). Cadmium showed toxicity at 5 mg L in case of root and shoot growth whereas 20 mg L in case of seed germination and germinat...

Introduction The use of contraception among currently married women in India has increased from 41 percent in 1992-93 to 56 percent in 2005-06, while the use of spacing method increased slowly; from 10 percent to 18 percent in the same period (IIPS and Macro International, 1995, 2000, and 2007). On the contrary about 27 percent of users of all methods in the country discontinued use within 12 m...

Story in Brief The phosphorus concentration in ruminal fluid was determined for steers limit-fed rations with phosphorus concentrations ranging from .06 to .17 percent. Ruminal phosphorus concentration was increased with phosphorus intake at dietary concentrations below .12 percent for steers. This relationship was employed to estimate the ruminal availability of phosphorus from four phosphorus...

This study was aimed at determining the effects of dietary zeolite (clinoptilolite) supplementation on fattening performance, slaughter characteristics, and some blood visceral organ parameters in Japanese quails. For this purpose, 140 (4x35) four-day-old quail chicks (Coturnix coturnix japonica) were randomly assigned to 4 groups with replicates (9+9+9+8), continued for a period 31 days. The f...

This thesis investigates uniform mixing on Cayley graphs over Z3. We apply Mullin’s results on Hamming quotients, and characterize the 2(d+2)-regular connected Cayley graphs over Z3 that admit uniform mixing at time 2π/9. We generalize Chan’s construction on the Hamming scheme H(d, 2) to the schemeH(d, 3), and find some distance graphs of the Hamming graph H(d, 3) that admit uniform mixing at t...

We begin with the simplest possible introduction to supergravity, and then discuss its spin 3/2 stress tensor. Next, we discuss boundary conditions on fields and boundary actions for N = 1 supergravity. Finally, we discuss new boundary contributions to the mass and central charge of monopoles in N = 4 super Yang-Mills theory. All models are in 3+1 dimensions. YITP-SB-06-21