77. Note on Question 309

A note on Fouquet-Vanherpe’s question and Fulkerson conjecture

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...

A Note on a Question of C .

Note on a Question of Reinhold Baer on Pregroups Ii

Reinhold Baer asked the relationship between certain properties in a nonempty set P with a partial operation (called an “add" by Baer [1]). The first paper in our sequence [Paper I] answered his question for a special type of an add called a pregroup by Stallings [12]. This paper [Paper II] answers an analogous question for a wider class of adds.

Note on a Question by S. Bagchi and B. Bagchi

In [l] Bagchi and Bagchi conjectured that one of the hypotheses of their theorem 2(d) is superfluous. This turns out to be true: PROPOSITION. Let 4 = 9 mod 16 be a prime power such that 2 is a fourth power in Fq. Then 1 f fi are nonsquares in Fp. Pruc$ Let p be a primitive eighth root of unity in Fq (note that /3 is a nonsquare). Because of (02 + 1)2 = p4 + 202 + 1 = 202 we obtain that (0 * + 1...

309 Dixon.qxd

ion. He will aim for general effects such as restoring lost self esteem to patients who may be as unable to cope with themselves as they are with their illnesses. Another long-term skill is the ability to induce a positive illness attitude and coping style, which may change the course of a patient’s life as well as his illness. Such skills have been shown to improve clinical status in a number ...