On the colorability of bi-hypergraphs

A {\it mixed hypergraph} ${\cal H}=({\cal V},{\cal C},{\cal D})$ consists of the vertex set ${\cal V}$ and two families of subsets of $2^{{\cal V}}$: the family ${\cal C}$ of co-edges and the family ${\cal D}$ of edges. ${\cal H}$ is said to be colorable if there is a mapping $f$ from ${\cal V}$ to the set of positive integers such that $|\{f(v):v\in e\}|<|e|$ for each $e\in {\cal C}$ and $|\{f(v):v\in e\}|>1$ for each $e\in {\cal D}$. There exist mixed hypergraphs which are uncolorable, and quite little about these mixed hypergraphs is known. A mixed hypergraph is called a bi-hypergraph if its co-edge set and edge set are the same. In this article, we first apply Lov\'asz local lemma to show that any $r$-uniform bi-hypergraph with $r\ge 4$ is colorable if every edge is incident to less than $(r-1)^{r-1}e^{-1}-1$ other edges, where $e$ is the base of natural logarithms. Then, we show that among all the uncolorable $3$-uniform bi-hypergraphs, the smallest size of a minimal one is ten, which answers a question raised by Tuza and Voloshin in 2000. As an extension, we provide a minimal uncolorable $3$-uniform bi-hypergraph of order $n$ and size at most $\frac{7n}3-4$ for every $n\ge 6$.Comment: 19 pages, 4 figure

Research on Quality and Flavor Characteristics of Five Kinds of Commercially Available Sour Fish Sauce in Qiandongnan

Five kinds of commercially available sour fish sauce were taken as the research object to clarify their quality and flavor characteristics. The physicochemical and nutritional indexes, free amino acids, and volatile components were analyzed. The results showed that the moisture, ash, total acid, amino acid nitrogen, reducing sugar, protein, vitamin C and fat contents in the five kinds of sour fish sauce were significantly different (P<0.05). In total, 17 free amino acids were detected, including 7 essential amino acids and 10 non-essential amino acids. The content of total free amino acids in the samples ranged from 7.954~14.998 mg/g. The total content of free amino acids in sample Z was the highest at 14.998 mg/g. The content of umami glutamic acid was the highest in the L sample, which was 4.689 mg/g, and the taste activity value (TAV) reached 15.63, which was much higher than that of other samples. The electronic nose results showed that the main volatile components of five kinds of sour fish sauce were nitrogen oxides, short-chain alkanes, inorganic sulfur compounds, alcohol ether aldehydes, and organic sulfides. Principal component analysis could differentiate between different sour fish sauces. In this study, 57 volatile components were detected in five kinds of sour fish sauce using gas chromatography-mass spectrometry (GC-MS), including 20 esters, 14 alcohols, 14 alkenes, 2 acids, 2 phenols, 3 aldehydes and 2 ketones. Using orthogonal least squares-discriminant analysis (OPLS-DA) and variable important projection (VIP) selection, eighteen key volatile aroma compounds, including zingalene, ethanol, ethyl cetanoate, ethyl linoleate, limonene, acetic acid, linalool, ethyl myristate, 4-ethyl-2-methoxyphenol, phenethyl alcohol, alpha-curcumene, methyl salicylate, β-sesquiphellandrene, citral, isoamyl alcohol, camphene, β-bisabolene and geraniol, were identified in the five kinds of sour fish sauce. In conclusion, the results provide a basis for the quality evaluation and comprehensive development of sour fish sauce

Golden pavilion of the Kongoji Temple（Kongō-ji 金剛寺）

The Kongoji Temple's Kondo (Kondo 金堂) was repaired in 2009 for the first time in 300 years.Non UBCUnreviewedAuthor Affiliation: International College for Postgraduate Buddhist StudiesGraduat

The main building of the nanatsudera temple (七寺)

The Nanatsudera Temple was built in 735 by Gyoki (行基), and the official name is Toenzan Shogakuin Chofukuji (稲園山正覚院長福寺). The Known name Nanatsudera (七寺) comes from seven monastery. However, due to the damage of World War II, the monastery other than Buddhist Sutra Storehouse was burned down.Non UBCUnreviewedAuthor Affiliation: International College for Postgraduate Buddhist StudiesGraduat

Iwayaji temple(岩屋寺) revolving bookshelf (Rinzo 輪蔵)

The revolving bookshelf within Buddhist Sutra Storehouse of Iwayaji temple(岩屋寺) was built in 1812.Non UBCUnreviewedAuthor Affiliation: International College for Postgraduate Buddhist StudiesGraduat

Old chest (Karabitsu 唐櫃) of nanatsudera temple(七寺)

The old chest (Karabitsu 唐櫃) of Nanatsudera temple(七寺) was made in 1175. There are 33 boxes. Currently there are 28 boxes in the temple, the other 6 boxes have been deposited at the museum.Non UBCUnreviewedAuthor Affiliation: International College for Postgraduate Buddhist StudiesGraduat

Zero-Free Intervals of Chromatic Polynomials of Mixed Hypergraphs

A mixed hypergraph H is a triple (X,C,D), where X is a finite set and each of C and D is a family of subsets of X. For any positive integer &lambda;, a proper &lambda;-coloring of H is an assignment of &lambda; colors to vertices in H such that each member in C contains at least two vertices assigned the same color and each member in D contains at least two vertices assigned different colors. The chromatic polynomial of H is the graph-function counting the number of distinct proper &lambda;-colorings of H whenever &lambda; is a positive integer. In this article, we show that chromatic polynomials of mixed hypergraphs under certain conditions are zero-free in the intervals (&minus;&infin;,0) and (0,1), which extends known results on zero-free intervals of chromatic polynomials of graphs and hypergraphs