Permutation Separations and Complete Bipartite Factorisations of $K_{n,n}$

10.37236/1730 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Nigel Martin ◽  
Richard Stong
Keyword(s):  

Suppose $p < q$ are odd and relatively prime. In this paper we complete the proof that $K_{n,n}$ has a factorisation into factors $F$ whose components are copies of $K_{p,q}$ if and only if $n$ is a multiple of $pq(p+q)$. The final step is to solve the "c-value problem" of Martin. This is accomplished by proving the following fact and some variants: For any $0\le k\le n$, there exists a sequence $(\pi_1,\pi_2, \dots,\pi_{2k+1})$ of (not necessarily distinct) permutations of $\{1,2,\dots,n\}$ such that each value in $\{-k,1-k,\dots,k\}$ occurs exactly $n$ times as $\pi_j(i)-i$ for $1\le j\le 2k-1$ and $1\le i\le n$.

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Febry Nugroho ◽  
Jamalludin Jamalludin ◽  
Elfi Indrawanis

Penelitian ini dilakukan di Desa Samber Datar Kecamatan Singingi Kabupaten Kuantan Singingi, Penelitian ini bertujuan untuk mengetahui besarnya pendapatan, efesiensi usaha R/C dan untuk mengetahui BEP produksi dan BEP harga pada usaha Agroindustri Keripik Tempe Djokam di Desa Sumber Datar Kecamatan Singingi Kabupaten Kuantan Singingi. Hasil penelitian ini menunjukan bahwa pendapatan keripik tempe djokam Rp 425.327/produksi dengan total biaya yang dikeluarkan sebesar Rp 574.673, yang terdiri dari biaya tetap dan biaya tidak tetap, nilai R/C sebesar 1,74, artinya setiap biaya yang dikeluarkan 1 rupiah maka diperoleh penerimaan sebesar 1,74 rupiah atau keuntungan sebesar 0,74 rupiah dan Break Even Poin produksi dengan total biaya sebesar Rp 574,673, maka harus memproduksi sebanyak 11,49 Kg dengan harga jualnya Rp 50.000, agar mencapai titik impas. Break Even Poin harga  dengan biaya sebesar Rp 574.673 maka Agroindustri Keripik Tempe harus memproduksi sebanyak 20 Kg dengan harga jual sebesar Rp 28.733, supaya mencapai titik impasnya.Kata Kunci : Agroindustri; Keripik Tempe; Pendapatan; R/C Ratio; BEP ABSTRACTThis research was conducted in Samber Datar Village, Singingi Subdistrict, Kuantan Singingi District. This study aims to determine the amount of revenue, efficiency of the R / C business and to determine the production BEP and price BEP in the Agroindustry of Tempe Djokam chips in Sumber Datar Village, Singingi District, Kuantan Singingi District. The results of this study indicate that the income of tempe chips djokam Rp 425,327 / production with a total cost incurred in the amount of Rp 574,673, consisting of fixed costs and variable costs, R / C value of 1.74, meaning that each cost incurred 1 rupiah is obtained revenue of 1.74 rupiahs or profit of 0.74 rupiahs and Break Even Points of production with a total cost of Rp 574,673, it must produce as much as 11.49 kg with a selling price of Rp 50,000, in order to break even. Break Even Price point at a cost of Rp 574,673 then the Tempe Chips Agroindustry must produce 20 kg with a selling price of Rp 28,733, in order to break even.Keywords: Agro-industry; Tempe Chips; Revenue; R / C Ratio; BEP


2019 ◽  
Vol 97 (Supplement_3) ◽  
pp. 241-242
Author(s):  
Yongjie Wang ◽  
Keshari Thakali ◽  
Sarah Shelby ◽  
Jason Apple ◽  
Yan Huang

Abstract The purpose of this study was to compare the meat quality and genomic differences between cross-bred commercial pig (CP) and domestic Large Black pig (BP). Seven cross-bred commercial pigs and eight British Large Black pigs were assigned to CP group and BP group, with initial mean body weights of 18.82±1.412 kg for CP group and 23.31±1.935 kg for BP group, P = 0.061, and fed ad libitum. The final BW of the CP at d101 was similar to the BP (130.0±8.16 kg vs. 121.1±2.80 kg, P = 0.132). However, the BP group took 108 days to reach the final BW. The ADG in the CP was higher than BP (1.102±0.0599 kg vs. 0.905±0.0138 kg, P = 0.003). The hot carcass weight of CP was higher (P &lt; 0.01) than BP, but the backfat of BP was higher (P &lt; 0.01) than CP. The a* value of CP was higher (P &lt; 0.05) than BP, and the c* value of CP was tended to be higher (P &lt; 0.10) than BP. However, the h value of BP was higher (P &lt; 0.05) than CP. The longissimus dorsi muscle fat content of BP was higher (P &lt; 0.05) than CP. For the fatty acid composition, the SFA and MUFA of BP were higher (P &lt; 0.05) than CP, but the PUFA of CP was higher (P &lt; 0.05) than BP. The metmyoglobin content of CP was tended to be higher (P &lt; 0.10) than BP. For the meat metabolism, the oxygen consumption of longissimus dorsi muscle of BP was higher (P &lt; 0.01) than CP. The RNA-Seq data showed that the expression of the genes related to lipid metabolism is higher in BP (fold change &gt; 3, P &lt; 0.05). To conclude, BP has higher meat quality, while CP has its advantages in growth performance. And the differences between these two breeds may due to the genomic diversity.


2021 ◽  
Vol 30 ◽  
pp. 2633366X2097865
Author(s):  
Li Jian

The surface treatment of carbon fibers (CFs) was carried out using a self-synthesized sizing agent. The effects of sizing agent on the surface of CFs and the interface properties of CF/polymethyl methacrylate (PMMA) composites were mainly studied. Scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and static contact angle were used to compare and study the CFs before and after the surface treatment, including surface morphology, surface chemical element composition, and wettability of the surface. The influence of sizing agent on the mechanical properties of CF/PMMA resin composite interface was investigated. The results show that after sizing treatment, the CF surface O/C value increased by 35.1% and the contact angles of CF and resin decreased by 16.2%. The interfacial shear strength and interlayer shear strength increased by 12.6%.


Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 284
Author(s):  
Ebru Bilici

With the advancement of technology in forestry, the utilization of advanced machines in forest operations has been increasing in the last decades. Due to their high operating costs, it is crucial to select the right machinery, which is mostly done by using productivity analysis. In this study, a productivity estimation model was developed in order to determine the timber volume cut per unit time for a feller-buncher. The Weibull distribution method was used to develop the productivity model. In the study, the model of the theoretical (estimated) volume distributions obtained with the Weibull probability density function was generated. It was found that the c value was 1.96 and the b value was 0.58 (i.e., b is the scale parameter, and c is the shape parameter). The model indicated that the frequency of the volume data had moved away from 0 as the shape parameter of the Weibull distribution increased. Thus, it was revealed that the shape parameter gives preliminary information about the distribution of the volume frequency. The consistency of the measured timber volume with the estimated timber volume strongly indicated that this approach can be effectively used by decision makers as a key tool to predict the productivity of a feller-buncher used in harvesting operations.


Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4091
Author(s):  
Zorana Kovačević ◽  
Ana Sutlović ◽  
Ana Matin ◽  
Sandra Bischof

In this study, the natural dye was extracted from Spartium junceum L. (SJL) flowers and applied on cellulose (cotton) and protein (wool) fabric. Fabrics were pre-mordant with alum prior to the dyeing process. Considering the global requirements on zero waste and green policy, the dyeing process was intended to be as much as possible environmentally friendly but still effective. Therefore, mordant concentration was optimized due to the reduction of the negative impact. The efficiency of the dyeing process was investigated by examination of fabrics’ color characteristics and colorfastness to washing properties. In this paper, we have proved that the extracted dye from Spartium junceum L. is an acidic dye (mordant dye) which is more applicable for the treatment of wool fabrics. In this paper, it was proved that phytochemicals responsible for coloring are part of the flavonoids group. The UV absorption spectra of extracted dye show 4 bands in the region of λmax 224, 268, 308 and 346 nm which are ascribed to bands characteristic for flavonoids. Wool fabric pre-mordant with 3% alum and dyed shows great chromatic (C*) properties where C* value is in a range from 47.76 for unwashed samples to 47.50 for samples after 5 washing cycles and color hue (h°) is in a range 82.13 for unwashed samples to 81.52 for samples after 5 washing cycles. The best result regarding the colorfastness properties is shown by the wool sample treated with 3% alum after 5 washing cycles (total difference in color (Delta E*) = 0.87). These results confirm that metal (Al) from alum mordant make strong chemical bonds with wool substrate and dye since Delta E* values decrease in comparison to Delta E* values of the cotton samples treated the same way. The results revealed it is possible to reduce the concentration of mordant up to 3% and obtain satisfactory results regarding the colorfastness. Nevertheless, future research will go in the direction of replacing synthetic mordant with a more environmentally friendly one.


1994 ◽  
Vol 42 (11) ◽  
pp. 1413-1416 ◽  
Author(s):  
S L Erlandsen ◽  
E M Rasch

We investigated direct measurement of the DNA content of the parasitic intestinal flagellate Giardia lamblia through quantitation by Feulgen microspectrophotometry and also by visualization of Feulgen-stained DNA chromosomes within dividing cells by laser scanning confocal microscopy. Individual trophozoites of Giardia (binucleate) contained 0.144 +/- 0.018 pg of DNA/cell or 0.072 pg DNA/nucleus. Giardia lamblia cysts (quadranucleate) contained 0.313 +/- 0.003 pg DNA or 0.078 pg DNA/nucleus. The genome size (C) value per nucleus ranged between 6.5-7.1 x 10(7) BP for trophozoites and cysts, respectively. Confocal microscopic examination of Giardia trophozoites undergoing binary fission revealed five chromosome-like bodies within each nucleus. Further information about genome size and DNA content within different Giardia species may help to clarify the pivotal role of these primitive eukaryotic cells in evolutionary development.


Radiocarbon ◽  
2008 ◽  
Vol 50 (3) ◽  
pp. 321-330 ◽  
Author(s):  
Supriyo Chakraborty ◽  
Koushik Dutta ◽  
Amalava Bhattacharyya ◽  
Mohit Nigam ◽  
Edward A G Schuur ◽  
...  

Radiocarbon analysis in annual rings of a teak tree (Tectona grandis) is reported in comparison with previously published results. Samples (disks) were collected from Hoshangabad (22°30′N, 78°E), Madhya Pradesh, in central India. The previously published sample was collected from Thane (19°12′N, 73°E), Maharashtra, near the west coast of India (Chakraborty et al. 1994). Two short Δ14C time series were reconstructed with these tree samples to capture the bomb peak of atmospheric 14C and the spatial variability in this record. These time series represent the periods 1954–1977 and 1959–1980 for Hoshangabad and Thane, respectively. The 14C peaks in these places appear around 1964–1965. The Hoshangabad tree records a peak Δ14C value of 708 ± 8%, which conforms to the peak value of Northern Hemisphere Zone 3 as described in Hua and Barbetti (2004). But the peak Δ14C at Thane is somewhat less (630 ± 8%) probably due to the dilution by fossil fuel CO2 free of 14C emanating from the neighboring industrial areas. This depletion of peak values has been used to estimate the local emission of fossil fuel CO2, which is approximately 2.3% of the background atmospheric CO2 concentration.


1995 ◽  
Vol 6 (8) ◽  
pp. 521-525 ◽  
Author(s):  
R. A. Van Den Bussche ◽  
J. L. Longmire ◽  
R. J. Baker
Keyword(s):  

2021 ◽  
pp. 1-23
Author(s):  
Jessica Z. Metcalfe ◽  
John W. Ives ◽  
Sabrina Shirazi ◽  
Kevin P. Gilmore ◽  
Jennifer Hallson ◽  
...  

The Promontory caves (Utah) and Franktown Cave (Colorado) contain high-fidelity records of short-term occupations by groups with material culture connections to the Subarctic/Northern Plains. This research uses Promontory and Franktown bison dung, hair, hide, and bone collagen to establish local baseline carbon isotopic variability and identify leather from a distant source. The ankle wrap of one Promontory Cave 1 moccasin had a δ13C value that indicates a substantial C4 component to the animal's diet, unlike the C3 diets inferred from 171 other Promontory and northern Utah bison samples. We draw on a unique combination of multitissue isotopic analysis, carbon isoscapes, ancient DNA (species and sex identification), tissue turnover rates, archaeological contexts, and bison ecology to show that the high δ13C value was not likely a result of local plant consumption, bison mobility, or trade. Instead, the bison hide was likely acquired via long-distance travel to/from an area of abundant C4 grasses far to the south or east. Expansive landscape knowledge gained through long-distance associations would have allowed Promontory caves inhabitants to make well-informed decisions about directions and routes of movement for a territorial shift, which seems to have occurred in the late thirteenth century.


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