Let $A$ be an abelian group. A graph $G=(V,E)$ is said to be $A$-barycentric-magic if there exists a labeling $l:E(G)longrightarrow Asetminuslbrace{0}rbrace$ such that the induced vertex set labeling $l^{+}:V(G)longrightarrow A$ defined by $l^{+}(v)=sum_{uvin E(G)}l(uv)$ is a constant map and also satisfies that $l^{+}(v)=deg(v)l(u_{v}v)$ for all $v in V$, and for some vertex $u_{v}$ adjacent t...

Let $(K,v)$ be a valued field and let $(K^h,v^h)$ the henselization determined by choice of an extension $v$ to algebraic closure $K$. Consider embedding $v(K^*)\hookrightarrow\Lambda$ value group into divisible ordered abelian group. $T(K,\Lambda)$, $T(K^h,\Lambda)$ trees formed all $\Lambda$-valued extensions $v$, $v^h$ polynomial rings $K[x]$, $K^h[x]$, respectively. We show that natural res...

The objective of this study was to evaluate the physical and chemical properties of the broiler feather concentrate (BFC) in different hydrolysis processes. The raw materials in the form of broiler feather waste (BFW) were hydrolyzed into broiler feather concentrate (BFC) products in the form of feather meal. A total of 1000 g of dry feather samples were used in this study. The study was design...