The breadth of a Lie algebra $L$ is defined to be the maximal dimension image $ad_x=[x,-]:L\to L$, for $x\in L$. Here, we initiate an investigation into three families algebras by posets and provide combinatorial formulas members each family.

Two families of 4-phase sequences are constructed using irreducible polynomials over Z4. Family d has period L = 2' 1, size L +2, and maximum nontrivial correlation magnitude C,,, 5 1 + m, where r is a positive integer. Family has period L = 2(2' l), size ( L + 2)/4, and C,,, 5 2 + m. Both families are asymptotically optimal with respect to the Welch lower bound on C,,, for complex-valued seque...

We construct the p-adic standard L-functions for ordinary families of Hecke eigensystems of the symplectic group Sp(2n)/Q using the doubling method. We explain a clear and simple strategy of choosing the local sections for the Siegel Eisenstein series on the doubling group Sp(4n)/Q, which guarantees the nonvanishing of local zeta integrals and allows us to p-adically interpolate the restriction...

We compute the universal deformations of cuspidal representations π of GL2(F ) over Fl, where F is a local field of residue characteristic p and l is an odd prime different from p. When π is supercuspidal there is an irreducible, two dimensional representation ρ of GF that corresponds to π via the mod l local Langlands correspondence of [Vi2]; we show that there is a natural isomorphism between...

Let H denote the set {f1, f2, ..., fn}, 2 the collection of all subsets of H and F ⊆ 2 be a family. The maximum of |F| is studied if any k subsets have a non-empty intersection and the intersection of any l distinct subsets (1 ≤ k < l) is empty. This problem is reduced to a covering problem. If we have the conditions that any two subsets have a non-empty intersection and the intersection of any...

Recent welfare reform legislation requires increased parental work effort and imposes time limits on the receipt of federal assistance. These changes were based in part on assumptions that parental welfare receipt may be negatively related to family processes and children's attitudes and behaviors. Currently, researchers know little about the effects of welfare by itself relative to the effects...

In August 1996, Congress and the president replaced the 60-year-old Aid to Families with Dependent Children (AFDC) program with a block grant, Temporary Assistance to Needy Families (TANF), permitting states to experiment with new forms of assistance to low-income families. States seem likely to try increasingly ambitious reforms as they gain experience under their TANF flexibility, at least if...

Let p be a prime > 2 and N be a positive integer with p 6 |N . Let f be a classical newform over Γ0(Np) of even weight k0 + 2 ≥ 2 and assume f is split multiplicative at p, thus ap(f) = p0 where ap(f) is the eigenvalue of the U -operator at p acting on f . Under these hypotheses, Coleman [3] defined an L-invariant L(f) which he conjectured to be equal to the higher weight Mazur-TateTeitelbaum L...

For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g. because of the Dirichlet class-number formula) and the symmetric square L-functions of ...