• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1855-1899
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• 2015

We discuss some additivity properties of the simplicial volume for manifolds with boundary: we give proofs of additivity for glueing amenable boundary components and of superadditivity for glueing amenable submanifolds of the boundary, and we discuss doubling of 3-manifolds.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.277-287
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• 2017

We consider ${\tau}_{\infty}(F)$ - the space of upper triangular infinite matrices over a field F. We investigate injective linear maps on this space which preserve the additivity of rank, i.e., the maps ${\phi}$ such that rank(x + y) = rank(x) + rank(y) implies rank(${\phi}(x+y)$) = rank(${\phi}(x)$) + rank(${\phi}(y)$) for all $x,\;y{\in}{\tau}_{\infty}(F)$.

• Journal of The Korean Society of Clinical Toxicology
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• v.3 no.1
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• pp.11-16
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• 2005

Chemical mixtures of components, each of which are present at less than guidance concentrations, may be hazardous due to additivity, interactions, or both. Toxicological interactions may increase the health hazard above what would be expected from an assessment of each component singly, or all components additively. So chemical mixture are a particular issue in public health. There are several approach to assess whether there are additivity or interaction in assessing toxicological effects, such as, components-based approach, physiologically-based pharmacokinetic /pharmacodynamic(PBPK/PD) models, hazard index method, and weight-of evidence method. If we consider interaction or additivity effects in assessing the health effects of chemcial mixtures, we can get more accurate information about toxicological effects and dose-response relationship in chemical mixtures.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.115-122
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• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.

• Asian-Australasian Journal of Animal Sciences
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• v.31 no.4
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• pp.564-568
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• 2018

Objective: This experiment was conducted to determine the effects of dietary ${\beta}$-mannanase on the additivity of true metabolizable energy (TME) and nitrogen-corrected true metabolizable energy ($TME_n$) for broiler diets. Methods: A total of 144 21-day-old broilers were randomly allotted to 12 dietary treatments with 6 replicates. Five treatments consisted of 5 ingredients of corn, wheat, soybean meal, corn distillers dried grains with solubles, or corn gluten meal. One mixed diet containing 200 g/kg of those 5 ingredients also was prepared. Additional 6 treatments were prepared by mixing 0.5 g/kg dietary ${\beta}$-mannanase with those 5 ingredients and the mixed diet. Based on a precision-fed chicken assay, TME and $TME_n$ values for 5 ingredients and the mixed diet as affected by dietary ${\beta}$-mannanase were determined. Results: Results indicated that when ${\beta}$-mannanase was not added to the diet, measured TME and $TME_n$ values for the diet did not differ from the predicted values for the diet, which validated the additivity. However, for the diet containing ${\beta}$-mannanase, measured $TME_n$ value was greater (p<0.05) than predicted $TME_n$ value, indicating that the additivity was not validated. Conclusion: In conclusion, the additivity of energy values for the mixed diet may not be guaranteed if the diet contains ${\beta}$-mannanase.

• Animal Bioscience
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• v.35 no.3
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• pp.453-460
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• 2022

Objective: The objective was to test additivity of digestible energy and nutrient concentrations in the hatchery byproduct mixture fed to nursery pigs. Methods: In the previous studies, energy, phosphorus, calcium, and amino acid digestibility of infertile eggs, unhatched eggs, culled chicks, and a mixture of 3 hatchery byproduct ingredients was determined in nursery pigs (initial body weight = 9.4 to 14.2 kg). An additivity test was conducted using these determined values. Results: No difference was observed between determined and predicted metabolizable energy values in the mixture (3,998 and 3,990 kcal/kg as-is basis, respectively). Measured standardized total tract digestible phosphorus in the mixture was less than the predicted value (4.5 vs 5.3 g/kg as-is basis, respectively; p<0.05). Measured standardized total tract digestible calcium in the mixture was greater compared with the predicted value (40.0 vs 31.7 g/kg as-is basis, respectively; p<0.05). Measured standardized ileal digestible tryptophan in the mixture was greater than the predicted value (3.7 vs 3.1 g/kg as-is basis, respectively; p<0.05) whereas other amino acid values were additive. Conclusion: Energy and most of amino acid concentrations in hatchery byproducts are additive in the mixture fed to nursery pigs.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.271-279
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• 2007

Let A standard operator algebra which does not contain the identity operator, acting on a Hilbert space of dimension greater than one. If ${\Phi}$ is a bijective Lie map from A onto an arbitrary algebra, that is $${\phi}$$(AB-BA)=$${\phi}(A){\phi}(B)-{\phi}(B){\phi}(A)$$ for all A, B${\in}$A, then ${\phi}$ is additive. Also, if A contains the identity operator, then there exists a bijective Lie map of A which is not additive.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.489-503
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• 2007

In this paper, we define signed interval-valued Choquet integrals which have numerous applications in mathematical economics, informatiom theory, expected utility theory, and risk analysis on interval-valued random variables, for examples: interval-valued random payments and interval-valued random profiles, etc. And we discuss axiomatic characterizations of them. Furthermore, we fine some condition that comonotonic additivity of symmetric Choquet integrals on interval-valued random payments is satisfied and give two examples related the main theorem.

• Applied Chemistry for Engineering
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• v.4 no.4
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• pp.709-714
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• 1993

The cetane number is a measure of ignition quality, specifically ignition delay, of diesel fuel. It is an engine measure of kinetic phenomena. The ignition quality such as kinetic behavior does correlate with the molecular structure, the carbon type structural composition. In fact, we use the group additivity rule to dissect the molecular structures and predict cetane number. In this study, the use of $^{13}C-Nuclear$ Magnetic Resonance spectroscopic measuring the molecular structure and group additivity rule at different diesel fuels, whose cetane numbers were determined on a number of standard cetane rating engines is proposed to predict cetane numbers that relate the carbon type structural composition. The effect of the molecular structures on the cetane numbers has been studied.

• Macromolecular Research
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• v.12 no.2
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• pp.246-250
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• 2004

We have classified a number of aqueous ternary systems containing two different polymers into three types by focusing on the deviation of the Huggins constant k'from the additivity line. Systems of type I have negative deviations of k'; the repulsive interaction between the two different polymers dominates. In systems of type II, k' almost follows the additivity relation; the repulsive and attractive interactions between the two different polymers are balancing. Type III systems have positive deviations of k'; the attractive interactions are relatively dominant. This classification of systems is supported by the fact that the positive and negative deviations of k' from the additivity line also correspond to the sign of interaction parameter between polymer 2 and 3, Δb$\_$23/. Furthermore, we have verified the relatively high compatibility between dextran and poly(vinyl alcohol) by determining the binodal concentration of a liquid-liquid phase separation for a water/dextran/poly(vinyl alcohol) system, which is classified as type III. Thus, we found that the compositional dependence of k' closely relates to the compatibility of binary polymer mixtures in aqueous ternary systems.