Two small, multicopy, expression plasmids were constructed that permit convenient Insert ion of trpR. the structural gene for the t r £ repressor of Escherichja c o l l . with I t s natural rlbosome binding s i te or adjacent to the Mbosome bindTn? s i te for the t r £ leader peptide. In these plasmids trpR 1s positioned between the strong regulated ta£ promoter and the rpoC transcr ipt ion ter...

As one aspect of the endeavor to c r e a te new i n t e l l e c t u a l t o o l s f o r mankind, we w ish to enable computers to p rove , and t o a s s i s t i n the p roo f s o f , theorems o f mathematics and ( e v e n t u a l l y ) o t h e r d i s c i p l i n e s which have ach ieved the r e q u i s i t e l o g i c a l p r e c i s i o n . For t h i s purpose, a p a r t i c u l a r l y s u i ...

The Hardy-Littlewood maximal operator satisfies the classical Sawyer-type estimate $$ \left \Vert \frac{Mf}{v}\right \Vert_{L^{1,\infty}(uv)} \leq C_{u,v} f \Vert_{L^{1}(u)}, where $u\in A_1$ and $uv\in A_{\infty}$. We prove a novel extension of this result to general restricted weak type case. That is, for $p>1$, A_p^{\mathcal R}$, $uv^p \in A_\infty$, \Vert_{L^{p,\infty}(uv^p)} \Vert_{L^{p,1}...

We discuss bound-states of D-branes in truly L-R asymmetric and thus non-geometric Type II vacuum configurations with extended supersymmetry. We argue for their stability as a result of residual supersymmetry and coupling to R-R potentials surviving in the massless spectrum. We then identify the open string excitations of these L-R asymmetric BPS D-branes. Finally, we briefly comment on possibl...

We study Sobolev mappings $f \in W_{\mathrm{loc}}^{1,n} (\mathbb{R}^n, \mathbb{R}^n)$, $n \ge 2$, that satisfy the heterogeneous distortion inequality \[\left|Df(x)\right|^n \leq K J_f(x) + \sigma^n(x) \left|f(x)\right|^n\] for almost every $x \mathbb{R}^n$. Here $K [1, \infty)$ is a constant and $\sigma \geq 0$ function in $L^n_{\mathrm{loc}}(\mathbb{R}^n)$. Although we recover class of $K$-qu...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of continuous real-valued functions on $L$. We study the frame $mathfrak{O}(Min(mathcal{R}L))$ of minimal prime ideals of $mathcal{R}L$ in relation to $beta L$. For $Iinbeta L$, denote by $textit{textbf{O}}^I$ the ideal ${alphainmathcal{R}Lmidcozalphain I}$ of $mathcal{R}L$. We show that sending $I$ to the set of minimal prime ...

The phage Mu transpososome is assembled by interactions of transposase subunits with the left (L) and right (R) ends of Mu and an enhancer (E) located in between. A metastable three-site complex LER progresses into a more stable type 0 complex in which a tetrameric transposase is poised for DNA cleavage. "Difference topology" has revealed five trapped negative supercoils within type 0, three co...