The size of the gel preparation, the concentration of the encapsulated enzyme and the ratio of the preparation volume to the volume of the reaction mixture influence the reaction efficiency with encapsulated biocatalysts. A model of first order enzymatic reaction with substrate diffusion is presented and validated by the decomposition reaction of hydrogen peroxide by catalase. The Thiele modulu...

a watching system in a graph $g=(v, e)$ is a set $w={omega_{1}, omega_{2}, cdots, omega_{k}}$, where $omega_{i}=(v_{i}, z_{i}), v_{i}in v$ and $z_{i}$ is a subset of closed neighborhood of $v_{i}$ such that the sets $l_{w}(v)={omega_{i}: vin omega_{i}}$ are non-empty and distinct, for any $vin v$. in this paper, we study the watching systems of line graph $k_{n}$ which is called triangular grap...

Let N be a non empty set with non empty elements and let S be an AMI over N . One can check that every finite partial state of S is finite. Let N be a non empty set with non empty elements and let S be an AMI over N . One can verify that there exists a finite partial state of S which is programmed. Next we state the proposition (1) Let N be a non empty set with non empty elements, and let S be ...

Let D be a non empty set and let E be a complex-membered set. One can verify that every element of D→̇E is complex-valued. Let D be a non empty set, let E be a complex-membered set, and let F1, F2 be elements of D→̇E. Then F1 + F2 is an element of D→̇C. Then F1 − F2 is an element of D→̇C. Then F1 · F2 is an element of D→̇C. Then F1/F2 is an element of D→̇C. Let D be a non empty set, let E be a comple...

suppose $f$ is a map from a non-empty finite set $x$ to a finite group $g$. define the map $zeta^f_g: glongrightarrow mathbb{n}cup {0}$ by $gmapsto |f^{-1}(g)|$. in this article, we show that for a suitable choice of $f$, the map $zeta^f_g$ is a character. we use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin g$) is a character, where $w(t_1,t...