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The authors determine the number of ( n + m )× t matrices A ∗ of rank r + v , over a finite field GF ( q ), whose last m rows are those of a given matrix A of rank r + v over GF ( q ) and whose first n rows have a given rank u .

Analogs are proved for sequences in Φ=GF[q, x], the ring of polynomials in x over a finite field of q elements, of results of Niven, Zane, and Cavior concerning uniform distribution of sequences of integers generated by polynomials with integer coefficients. The uniform distribution (mod m), m an integer, in these papers is replaced here by a concept called weak uniform distribution (mod M), M e Φ.

Explicit formulas are found for the number of solutions over a finite field of several matrix equations, for example:X′A+A′X=B. Conditons for solvability are also given.

An expression is derived for the number of representations of one bilinear form by another (mod pa). From this, an explicit formula for the number of such representations is obtained in the case where both forms have square nonsingular matrices (mod p). A related bilinear analog of a lemma of Siegel on representations by quadratic forms (mod pa) is also proved.

Analogs are proved for sequences in Φ=GF[q, x] and Φ′=GF {q, x } of results proved in 1962 by C.L. Vanden Eynden concerning uuiform distribution of sequence of integers related to sequences of real numbers. The concept of uniform distribution (mod m), m an integer, in Vanden Eynden's work is sometimes replaced here by modified forms of uniform distribution (mod M) M ∈ Φ.

SummaryAttempts to isolate a filtrable infectious agent from adult patients with epidemic diarrhea, nausea, and vomiting were unsuccessful. We were unable to duplicate the results of Light and Hodes. Perhaps the virus had disappeared during preservation of the frozen stools, or was never present in the stools, or insufficient amounts of inoculum were used, or the disease in adults with which we dealt is different from that in the newborn.

SummaryAmong the 32 volunteers who inhaled nebulized filtered garglings, symptoms developed in 17; of the 21 who inhaled nebulized stool filtrates, 11 developed symptoms. Of the combined groups of 53 volunteers, 28 (53%) developed symptoms as compared with 22 out of 240 (9%) of the rest of the student body in which the natural disease apparently occurred during the period of the tests. No attacks occurred in 6 volunteers who inhaled serum nor in 24 volunteers who were fed serum or filtrates of garglings or stools.The results, considering the unideal circumstances during which the tests had to be made, suggest that the causative agent of the disease is filtrable, airborne, enters through the respiratory tract and is present in the oropharynx and stool but not in the blood. Tests are now being made in a nonepidemic period with material from the November epidemic preserved at −70°C.

From the few reports of similar large and small outbreaks of a mild acute gastrointestinal disturbance observed in the United States,1Germany,2Canada,3England,4Denmark,5Australia6and elsewhere, one would gain the impression that it is an uncommon "new" disease entity. It is almost certain, however, that it is a widespread, communicable, endemic, sporadic and at times epidemic disease or group of diseases, apart from the known forms of dysentery and acute food poisoning, which because of its mildness usually passes unnoted in the press of other problems. In our experience, cases or groups of cases similar to those described have been casually observed for years. Most of the reported epidemics among adults occurred in schools, barracks, hospitals and hotels where the number, not the severity, of cases attracted attention and provoked inquiry. The majority of patients are not sick severely enough or long