‎given a finite non-cyclic group $g$‎, ‎call $sigma(g)$ the smallest number of proper subgroups of $g$ needed to cover $g$‎. ‎lucchini and detomi conjectured that if a nonabelian group $g$ is such that $sigma(g) < sigma(g/n)$ for every non-trivial normal subgroup $n$ of $g$ then $g$ is textit{monolithic}‎, ‎meaning that it admits a unique minimal normal subgroup‎. ‎in this paper we show how thi...

let $g$ be a simple graph with an orientation $sigma$‎, ‎which ‎assigns to each edge a direction so that $g^sigma$ becomes a‎ ‎directed graph‎. ‎$g$ is said to be the underlying graph of the‎ ‎directed graph $g^sigma$‎. ‎in this paper‎, ‎we define a weighted skew‎ ‎adjacency matrix with rand'c weight‎, ‎the skew randi'c matrix ${bf‎ ‎r_s}(g^sigma)$‎, ‎of $g^sigma$ as the real skew symmetric mat...

Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...

A Hindu Brahmin, a lawyer by profession, aged 70 years, noticed the onset of the following symptoms in July 1930. Both his mental and physical vigour gradually deteriorated until he finally lost all interest in life both in his work and pleasure. His appetite was poor and he suffered from obstinate constipation, but apart from these symptoms no physical cause for his condition could be discover...

exp or(lered alkaline drauglits to be given, believing that es81v? acidity of the stomach was the cause : several doses were eQ without any beneficial result. call'V evening, acute dysentery set in, the patient being ed to tho stool from 10 to 14 times during the night. Next lie r-ain^ &ave him a scruple of ipecacuanha in the hope of rel'10 patient of his obstinate hiccough, but it gave him no ...

History of present illness.?Three days previously the Patient had a sudden attack of vomiting and purging flowed the next day by flatulence and constipation. Ahe abdominal distension went on increasing and the constipation became obstinate without any flatus being Passed. There was, .however, no more vomiting, though r jlrs.t and nausea were prominent complaints. Enemata, administered at the ru...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...