• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.227-245
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• 2014

Suppose G is a simple graph. The ${\ell}$-eigenvalues ${\delta}_1$, ${\delta}_2$,..., ${\delta}_n$ of G are the eigenvalues of its normalized Laplacian ${\ell}$. The normalized Laplacian Estrada index of the graph G is dened as ${\ell}EE$ = ${\ell}EE$(G) = ${\sum}^n_{i=1}e^{{\delta}_i}$. In this paper the basic properties of ${\ell}EE$ are investigated. Moreover, some lower and upper bounds for the normalized Laplacian Estrada index in terms of the number of vertices, edges and the Randic index are obtained. In addition, some relations between ${\ell}EE$ and graph energy $E_{\ell}$(G) are presented.

• Asian-Australasian Journal of Animal Sciences
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• v.33 no.6
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• pp.1034-1041
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• 2020

Objective: The objective of this experiment was to evaluate the effect of shade allocation and shade plus fan on growth performance, dietary energy utilization and carcass characteristics of feedlot cattle under tropical ambient conditions Methods: Two trials were conducted, involving a total of 1,560 young bulls (289±22 kg BW) assigned to 24 pens (65 bulls/pen and 6 pens/treatment). Pens were 585 ㎡ with 15 m fence line feed bunks. Shade treatments (㎡ shade/animal) were: i) limited shade (LS) to 1.2 ㎡ shade/animal (LS_1.2); ii) limited shade to 2.4 ㎡ shade/animal (LS_2.4); iii) total shade (TS) which correspond to 9 ㎡/animal, and iv) total shade equipped with fans (TS+F). Trials lasted 158 and 183 days. In both studies, the average weekly maximum temperature exceeded 34℃. Results: Increasing shade allocation tended (p = 0.08) to linearly increases average daily gain (ADG), and dry matter intake (DMI, quadratic effect, p = 0.03). This effect was most apparent between LS_1.2 and LS_2.4. Shade allocation, per se, did not affect gain efficiency or estimated dietary net energy (NE). Compared with TS, TS+F increased (p<0.05) ADG, gain efficiency, and tended (p = 0.06) to increase dietary NE. There was a quadratic effect of shade on longissimus area and marbling score, with values being lower (p<0.01) for LS_2.4 than for LS_1.2 or TS. Likewise, marbling score was lower for TS+F than for TS. Percentage kidney, pelvic, and heart (KPH) linearly decreased with increasing shade. In contrast, KPH was greater for TS than for TS+F. Conclusion: Providing more than 2.4 ㎡ shade/animal will not further enhance feedlot performance. The use of fans in combination with shade increases ADG and gain efficiency beyond that of shade, alone. These enhancements were not associated with increased DMI, but rather, to an amelioration of ambient temperature humidity index on maintenance energy requirement.

• Asian-Australasian Journal of Animal Sciences
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• v.29 no.5
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• pp.652-658
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• 2016

Twenty $Pelibuey{\times}Katahdin$ ewes ($35{\pm}2.3kg$) were used to determine the effects of the consumption of standardized plant extract containing a mixture of quaternary benzophenanthridine alkaloids and protopine alkaloids (QBA+PA) on growth performance, dietary energetics, visceral mass, and ruminal epithelial health in heat-stressed ewes fed with a high-energy corn-based diet. The basal diet (13.9% crude protein and 2.09 Mcal of net energy [NE] of maintenance/kg of dry matter) contained 49.7% starch and 15.3% neutral detergent fiber. Source of QBA+PA was Sangrovit RS (SANG) which contains 3 g of quaternary benzophenathridine and protopine alkaloids per kg of product. Treatments consisted of a daily consumption of 0 or 0.5 g SANG/ewe. Ewes were grouped by weight and assigned to 10 pens (5 pens/treatment), with two ewes per pen. The experimental period lasted 70 days. The mean temperature humidity index during the course of this experiment was $81.7{\pm}1.0$ (severe heat stress). There were no treatment effects on water intake. Dry matter intake was not affected (p = 0.70) by treatments, but the group fed SANG had a numerically (11.2%) higher gain in comparison to the control group, SANG improved gain efficiency (8.3%, p = 0.04), dietary NE (5.2%, p<0.01) and the observed-to-expected NE (5.9%, p<0.01). Supplemental SANG did not affect ($p{\geq}0.12$) carcass characteristics, chemical composition of shoulder, and organ weights (g/kg empty body weight) of stomach complex, intestines, and heart/lung. Supplemental SANG decreased liver weight (10.3%, p = 0.02) and increased visceral fat (16.9%, p = 0.02). Rumen epithelium of ewes fed SANG had lower scores for cellular dropsical degeneration (2.08 vs 2.34, p = 0.02), parakeratosis (1.30 vs 1.82, p = 0.03) and neutrophil infiltration (2.08 vs 2.86, p = 0.05) than controls. It is concluded that SANG supplementation helped ameliorate the negative effects of severe heat on growth performance of feedlot ewes fed high-energy corn-based diets. Improvement in energetic efficiency may have been mediated, in part, by anti-inflammatory effects of supplemental SANG and corresponding enhancement of nutrient uptake.

• Asian-Australasian Journal of Animal Sciences
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• v.26 no.11
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• pp.1553-1561
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• 2013

Forty-eight crossbred heifers ($378.1{\pm}18$ kg) were used in a 56-d feeding trial (four pens per treatment in a randomised complete block design) to evaluate the influence of ionophore supplementation on growth performance, dietary energetics and carcass characteristics in finishing cattle during a period of heat stress. Heifers were fed a diet based on steam-flaked corn (2.22 Mcal $NE_m/kg$) with and without an ionophore. Treatments were: i) control, no ionophore; ii) 30 mg/kg monensin sodium (RUM30); iii) 20 mg/kg lasalocid sodium (BOV20), and iv) 30 mg/kg lasalocid sodium (BOV30). Both dry matter intake (DMI) and climatic variables were measured daily and the temperature humidity index (THI) was estimated. The maximum THI during the study averaged 93, while the minimum was 70 (THI average = $79.2{\pm}2.3$). Compared to controls, monensin supplementation did not influence average daily gain, the estimated NE value of the diet, or observed-to-expected DMI, but tended (p = 0.07) to increase (4.8%) gain to feed. Compared to controls, the group fed BOV30 increased ($p{\leq}0.03$) daily gain (11.8%), gain to feed (8.3%), net energy of the diet (5%), and observed-to-expected DMI (5.2%). Daily weight gain was greater (7.6%, p = 0.05) for heifers fed BOV30 than for heifers fed MON30. Otherwise, differences between the two treatments in DMI, gain to feed, and dietary NE were not statistically significant (p>0.11). Plotting weekly intakes versus THI, observed intake of controls was greater (p<0.05) at THI values ${\leq}77$ than ionophore groups. When THI values were greater than 79, DMI of control and MON30 were not different (p = 0.42), although less than that of groups fed lasalocid (p = 0.04). Variation in energy intake was lower (p>0.05) in the ionophores group (CV = 1.7%) than in the control group (CV = 4.5%). Inclusion of ionophores in the diet resulted in relatively minor changes in carcass characteristics. It is concluded that ionophore supplementation did not exacerbate the decline of DM intake in heat-stressed cattle fed a high-energy finishing diet; on the contrary, it stabilised feed intake and favoured feed efficiency. Ionophore supplementation reduced estimated maintenance coefficients around 10% in finishing cattle during a period of heat stress. This effect was greatest for heifers supplemented with 30 mg lasalocid/kg of diet.