‎There are a few finite groups that are determined up to isomorphism solely by their order, such as $mathbb{Z}_{2}$ or $mathbb{Z}_{15}$. Still other finite groups are determined by their order together with other data, such as the number of elements of each order, the structure of the prime graph, the number of order components, the number of Sylow $p$-subgroups for each prime $p$, etc. In this...

We investigate the theory IAo + Q, and strengthen [Bu86. Theorem 8.6] to the following: if NP 7 co-NP. then 1-completeness for witness comparison foumulas is not provable in bounded arithmetic.

In this paper we study the local behavior of a solution to the Lamé system with Lipschitz coefficients in dimension n ≥ 2. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lamé system with Lipschitz coefficients...

In this paper we determine a characteristic class of ILsetframes for the principle F. Then we prove that the principle P is not provable in the system ILF. We use a generalized Veltman model.

We establish an information theoretic inequality concerning the binary skew-symmetric channel that was conjectured in [1]. This completes the proof that there is a gap between the inner bound[2] and the outer bound[3] for the 2receiver broadcast channel; and constitutes the first example of a provable gap between the bounds. The interesting aspect of the proof is the technique employed, and is ...

In this paper it is shown that addition of certain reductions to the standard cut removing reductions of deductions in propositional logic makes propositional logic non-normalizable. From this follows that some provable propositions in propositional logic has no direct proof.

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....