let $l$ be a lattice in $zz^n$ of dimension $m$. we prove that there exist integer constants $d$ and $m$ which are basis-independent such that the total degree of any graver element of $l$ is not greater than $m(n-m+1)md$. the case $m=1$ occurs precisely when $l$ is saturated, and in this case the bound is a reformulation of a well-known bound given by several authors. as a corollary, we show t...

reaction of 5-phenyl tetrazole with ethyl chloroacetate to form ethyl (5-phenyl-1h-tetrazol-1-yl) acetate (1). compound 1 react with hydrazine hydrate in ethanol yield 2-(5-phenyl-1h-tetrazol-1-yl) acetohydrazide (2). the condensation of (2) with various aldehydes yield the corresponding substituted n'-[-arylidene]-2-(5-phenyl-1h-tetrazol-1-yl) acetohydrazide (3a- j). the compounds obtaine...

Let X be a set of vectors in R m. X is said to be a Hilbert base if every vector in R m which can be written both as a linear combination of members of X with nonnegative coeecients and as a linear combination with integer coeecients can also be written as a linear combination with nonnegative integer coeecients. Denote by H the collection of the graphs whose family of cuts is a Hilbert base. I...