Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$. It is the graph with all elements of £ as vertices, and for distinct $x, y in £$, the vertices $x$ and $y$ are adjacent if and only if $x vee y in {rm Z}(£)$. The basic properties of the ...

For nonzero vectors x and y in the normed linear space (X ,‖·‖) we can define the p -angular distance by αp [x,y] := ∥∥‖x‖p−1 x−‖y‖p−1 y ∥∥ . In this paper we show among others that 1 2 ∣∣ ∣∣‖x‖p−1−‖y‖p−1 ∣∣‖x+ y‖− ( ‖x‖p−1 +‖y‖p−1 ) ‖x− y‖ ∣∣ αp [x,y] 1 2 ∣∣‖x‖p−1 −‖y‖p−1 ∣∣‖x+ y‖+ ( ‖x‖p−1 +‖y‖p−1 ) ‖x− y‖ ] for any p ∈ R and for any nonzero x,y ∈ X . Some reverses of the triangle and the con...

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

The structure of hadrons consisting of three static color sources in fundamental (baryons) or adjoint (three-gluon glueballs) representations is studied. The static potentials of glueballs as well as gluon field distributions in glueballs and baryons are calculated in the framework of field correlator method. 1. The study of the gluon field structure in hadrons is important for the deep underst...

In a recent note [1] appearing in this Monthly, Chen and Choi calculated a j in 1 + 1 x x = e ∞ j=0 a j x j (1) We offer a briefer calculation of these same coefficients. Applying the change of variables y = 1 x , and the two functions f (y) = e y , g(y) = ln(1+y) y , we rewrite (1) as f (g(y)) = ∞ j=0 (ea j)y j We take derivatives of this formal power series j times, and substitute y = 0, to g...