Ternary Term Research Articles

The clinical impact of frailty on the postoperative outcomes of patients undergoing appendectomy: propensity score-matched analysis of 2011-2017 US hospitals.

The presence of clinical frailty can pose an escalated risk toward surgical outcomes including in cases that involve minimally invasive procedures. Given this premise, we evaluate the effects of frailty on post-appendectomy outcomes using a national in-hospital registry. 2011-2017 National Inpatient Sample was used to isolate inpatient appendectomy cases; the population as stratified using Johns Hopkins ACG clinical frailty, expressed as either binary or ternary (prefrailty, frailty, and without frailty) indicators. The controls were matched to frailty-present groups using propensity score matching and compared to various endpoints, including mortality, length of stay (LOS), hospitalization costs, and postoperative complications. Post-match, there were 11,758 with and without frailty per binary; and 1236 frail, 10,522 pre-frail with respective equal number controls per ternary indicator. Using binary term, frail patients had higher mortality (4.22 vs 1.49% OR 2.92 95%CI 2.45-3.47), LOS (14.3 vs 5.35d p < 0.001), and costs ($160,700 vs $64,141 p < 0.001). In multivariate, frail patients had higher mortality (aOR 2.77 95%CI 2.32-3.31), as well as higher rates of postoperative complications. Using ternary term, frail patients had higher mortality (5.02 vs 2.27% OR 2.28 95%CI 1.45-3.59), LOS (18.9 vs 5.66 day p < 0.001) and costs ($200,517 vs $66,193 p < 0.001). In multivariate, frail patients had higher mortality (aOR 2.16 95%CI 1.35-3.43) and complications. Those with pre-frailty had higher mortality (4.12 vs 1.47% OR 2.88 95%CI 2.39-3.46), LOS (13.8 vs 5.34 day p < 0.001) and costs ($156,022 vs $63,772 p < 0.001). In multivariate, pre-frailty patients had higher mortality (aOR 2.79 95%CI 2.31-3.37) and complications. Frailty and prefrailty (using the ternary indicator) are associated with increased postoperative mortality and complication in patients who undergo appendectomy; given this finding, it is imperative that these vulnerable patients are identified early in the preoperative phase and are provided risk-modifying measures to ameliorate risks and optimize outcomes.

Phase equilibria and volumetric and viscosity behavior of the aqueous double salt ionic liquid [EMIM][SCN]x[MeSO3](1-x)

Continuing our recent systematic studies on thermodynamic and thermophysical properties of binary aqueous ionic liquids (ILs), this work extends our investigations to aqueous double salt ionic liquids (DSILs). Specifically, the (water + [EMIM][SCN]x[MeSO3](1-x)) system is examined here: vapor-liquid and solid-liquid equilibria, volumetric and viscosity behaviors were experimentally determined at three DSIL compositions (x approx. 0.75, 0.5, and 0.25 or 0.20) and several water contents xw. Water activity was measured at seven temperatures from (288.15 to 318.15) K and for xw from 0.3 to 1, freezing temperature for xw from 0.8 to 1, density and dynamic viscosity at two temperatures (298.15 and 323.15 K) and for xw from 0 to 0.9. The acquired data were treated as those for the ternary system (water + [EMIM][SCN] + [EMIM][MeSO3]) and modeled coherently together with its binary subsystems. The ternary water activity data were successfully correlated by the extended NRTL model, adopting for the aqueous parent IL binaries the parameters we evaluated previously, and fitting just those remaining for the (IL + IL) pair. The established model was shown to predict perfectly the measured SLE data. This model further provides an otherwise hardly procurable insight into the energetics of the DSIL. As inferred from the model, the ([EMIM][SCN] + [EMIM][MeSO3]) binary system exhibits quite large positive deviations from ideality, its excess Gibbs energy stemming from the very endothermic mixing of the two ILs which is only partially compensated by the positive excess entropy. The (IL + IL) mixture exhibits a positive, but very small excess volume, only slightly increasing as temperature increases, while its viscosity is much greatly affected by both temperature and the DSIL composition. The viscosity deviation from the linear mixing rule is for the DSIL negative and large but obeying quite accurately the linear mixing rule of logarithmic viscosity. For the aqueous mixtures of both parent ILs, the logarithmic viscosity deviation is high and greatly composition asymmetric. Coherent and sufficiently accurate representation of the volumetric and viscosity data for the ternary system and all its binary subsystems was achieved by Padé approximants with temperature-dependent parameters amended with a ternary term. Compared to the neat [EMIM][MeSO3], [EMIM][SCN]x[MeSO3](1-x) with smaller contents of [EMIM][SCN] (x < 0.2) and water (xw < 0.2) shows higher water affinity, while having considerably lower viscosity. Thus, the use of this DSIL as a water absorption medium for desiccation and cooling applications was found to be very beneficial.

Deciding the Existence of Minority Terms

AbstractThis paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation $m$ that satisfies the minority equations $m(y,x,x)\approx m(x,y,x)\approx m(x,x,y)\approx y$. We show that a common polynomial-time approach to testing for this type of condition will not work in this case and that this decision problem lies in the class NP.

Selfextensional logics with a distributive nearlattice term

We define when a ternary term m of an algebraic language $$\mathcal {L}$$ is called a distributive nearlattice term ( $$\mathrm {DN}$$ -term) of a sentential logic $$\mathcal {S}$$ . Distributive nearlattices are ternary algebras generalising Tarski algebras and distributive lattices. We characterise the selfextensional logics with a $$\mathrm {DN}$$ -term through the interpretation of the DN-term in the algebras of the algebraic counterpart of the logics. We prove that the canonical class of algebras (under the point of view of Abstract Algebraic Logic) associated with a selfextensional logic with a $$\mathrm {DN}$$ -term is a variety, and we obtain that the logic is in fact fully selfextensional.

Simultaneous VLLE data correlation for ternary systems: Modification of the NRTL equation for improved calculations

Simultaneous correlation of vapour–liquid–liquid equilibrium (VLLE) data is hardly ever attempted in literature with one common set of parameters for all the equilibrium regions present in the systems. It is common practice to obtain different sets of parameters for VLE, LLE and VLLE regions when experimental equilibrium data for ternary systems are fitted with a given model (e.g. an activity coefficient model for the liquid phase). Besides, when dealing with the correlation of VLE for ternary systems, it is quite frequent to obtain different sets of parameters for each one of the three binary subsystems from those obtained when exclusively binary VLE data are correlated. In the present work, the simultaneous correlation of all the equilibrium regions in the ternary VLL system is attempted. The objective function and the restrictions of the system are clearly presented. In addition, a simple modification of the NRTL equation for the Gibbs energy of mixing (GM) is proposed including a ternary term and a binary correction based on the Wohl equation. This modification has significantly improved the quality of the results obtained in the simultaneous correlation of different equilibrium regions.

Experimental Data and Correlation of Surface Tensions of the Binary and Ternary Systems of Water + Acetonitrile + 2-Propanol at 298.15 K and Atmospheric Pressure

This paper reports the results of a new experimental study of surface tension for the ternary mixtures of water/acetonitrile/2-propanol. Correlating the excess surface tension of the above-mentioned binary and ternary systems was performed with empirical and thermodynamic based models. The methods of Pando et al. and Ku et al. were used to correlate the ternary surface tension data. The ternary surface tension data were well-correlated using pair additivity and rational functions as the ternary term. The results provide information on the molecular interactions between the unlike molecules that exist at the surface and the bulk.

2-uniform congruences in majority algebras and a closure operator

A ternary term m(x, y, z) of an algebra is called a majority term if the algebra satisfies the identities m(x, x, y) = x, m(x, y, x) = x and m(y, x, x) = x. A congruence α of a finite algebra is called uniform if all of its blocks (i.e., classes) have the same number of elements. In particular, if all the α-blocks are two-element then α is said to be a 2-uniform congruence. If all congruences of A are uniform then A is said to be a uniform algebra. Answering a problem raised by Gratzer, Quackenbush and Schmidt [2], Kaarli [3] has recently proved that uniform finite lattices are congruence permutable.

On tractability and congruence distributivity

Constraint languages that arise from finite algebras have recently been the object of study, especially in connection with the Dichotomy Conjecture of Feder and Vardi. An important class of algebras are those that generate congruence distributive varieties and included among this class are lattices, and more generally, those algebras that have near-unanimity term operations. An algebra will generate a congruence distributive variety if and only if it has a sequence of ternary term operations, called Jonsson terms, that satisfy certain equations. We prove that constraint languages consisting of relations that are invariant under a short sequence of Jonsson terms are tractable by showing that such languages have bounded relational width.

An optimal method to calculate the viscosity of simple liquid ternary alloys from the measured binary data

An optimal method to calculate the viscosity of simple liquid ternary alloys from the measured binary data is investigated in this paper. In order to find a relationship which describes the ternary viscosity data from binary data most adequately, a comparison was made between three different approaches tested on the example of the Au–Ag–Cu system. The optimal method turned out to be the extension of the Redlich–Kister polynomial to excess viscosity without any ternary term. This optimal method was applied further on the Fe–Ni–Co system. The estimation of viscosities for liquid Fe–Ni–Co alloys was done in different sections with molar ratio of two components equal to 1:1, 1:3 and 3:1. A diagram showing iso-viscosity lines was constructed at the investigated temperature of 1873 K.

Semilattice Operations Generated by Lattice Terms

Let ℒ=〈L;∨,∧〉 be a subdirectly irreducible modular lattice, c∈L and p(x,y,z) an essentially ternary lattice term. In this paper we show that if p(x,y,c) is a semilattice operation then p(x,y,c)=∨ or ∧ and L is bounded and c=0 or c=1. This sheds light on the methodology used to move back and forth between generalizations of median algebras and lattices, and provides a negative answer to a problem posed by A. Knoebel and G. Meletiou.

Bands with a small number of ternary term functions

Bands with a small number of ternary term functions

A Kiss 4-difference term from a ternary term

A Kiss 4-difference term from a ternary term

Commutator Theory Without Join-Distributivity

We develop Commutator Theory for congruences of general algebraic systems (henceforth called algebras) assuming only the existence of a ternary term $d$ such that $d(a,b,b)[\alpha ,\alpha ]a[\alpha ,\alpha ]d(b,b,a)$, whenever $\alpha$ is a congruence and $a\alpha b$. Our results apply in particular to congruence modular and $n$-permutable varieties, to most locally finite varieties, and to inverse semigroups. We obtain results concerning permutability of congruences, abelian and solvable congruences, connections between congruence identities and commutator identities. We show that many lattices cannot be embedded in the congruence lattice of algebras satisfying our hypothesis. For other lattices, some intervals are forced to be abelian, and others are forced to be nonabelian. We give simplified proofs of some results about the commutator in modular varieties, and generalize some of them to single algebras having a modular congruence lattice.

Thermodynamic studies and phase diagrams of the Cd-Ga-In system

Calorimetric and vapor pressure data of liquid Cd- Ga- In alloys were measured. From these data an optimized set of thermodynamic parameters of the Cd- Ga- In system was derived using the leastsquares method. The thermodynamic parameters of the binary subsystems were taken from the literature and combined to a ternary description by the Muggianu formula. This description was augmented by a ternary term for the liquid phase, described as a function of temperature and concentration by six coefficients.

A computer assessment of the ternary Ru-Rh-Pd system

Abstract Thermodynamic coefficients of the phases in the binary Ru-Rh, Pd-Rh and Ru-Pd systems were derived by assessment of the available experimental data using the binary Lukas optimization program. The resulting coefficients were first successfully utilised in re-establishing the binaries. The coefficients thus established in the binary computation were combined with binary descriptions to compute ternary isothermal sections. Although no ternary interaction term was involved in the construction of the isotherms, the calculation at 1973 K is found to be consistent with the experimentally established isothermal section at the same temperature. The location of three-phase fields (liquid + hcp + fcc) and phase boundaries in both isotherms are matching reasonably well and these show that that ternary interactions of the components in these phases are less strong. Combining only binary coefficients of these phases it is possible to construct reasonable isothermal sections at different temperatures. Following this conclusion, isothermal sections ranging from 973 to 2473 K of the ternary Ru-Rh-Pd system were calculated.

Phase Equilibria in the Water-Methyl Alcohol-Methyl tert-Butyl Ether-Ethylene Glycol System

Liquid-liquid equilibria were measured at 20 °C in the W-MeOH-MTBE-EG quaternary system (W is water, MeOH is methyl alcohol, MTBE is methyl tert-butyl ether, and EG is ethylene glycol) and in the W-MeOH-MTBE, W-MTBE-EG and MeOH-MTBE-EG ternary systems. In the W-MeOH-MTBE-EG, W-MeOH-MTBE, and MeOH-MTBE-EG systems, the vapour-liquid equilibria at atmospheric pressure were also measured. The experimental data of the quaternary system were compared with those modelled by superposition of the Wilson and Redlich-Kister equations with the ternary term, whose parameters were determined based on the corresponding binary and, in some cases, ternary systems. A very good agreement was obtained for both the liquid-liquid and vapour-liquid equilibria.

Liquid-liquid equilibrium in the water-ethanol-toluene system. Correlation of equilibrium data

Liquid-liquid equilibrium data in the water-ethanol-toluene system were correlated by the superposition of the Wilson and Redlich-Kister equations with a ternary term. The correlation of both homogeneous binary systems was taken from the literature. The ternary liquid-liquid equilibrium data were at all temperatures satisfactorily described on using only three ternary parameters determined from the equilibrium data at 50 °C. The parameters obtained by the correlation yield also a good estimate of boiling point and composition of homogeneous azeotropic mixture.

Determination of ternary vlle by p(x 1,x 2) measurements

For determination of VLE and LLE of ternary systems showing a misciblity gap the static method of p(x 1,x 2) measurements at constant temperature has been applied. The apparatus used is similar to that described by Gibbs and Van Ness. Measurements have been carried out for the system ethanol/water/cyclohexane at 303.15 K. For data reduction Barker's method has been chosen. The excess Gibbs energy is represented by a NRTL-equation with an added ternary term. Because this mixture behaves strongly non-ideal a representation of the data was not possible for the entire range of composition with one set of parameters. Therefore, data reduction had to be carried out separately for limited regions. Thus, a fairly good representation of both VLE and LLE could be achieved.

The effect of specific interactions on the sorption equilibrium in the polymer/mixed solvent system

AbstractUsing the theory of association equilibria, equations are derived for preferential and total sorption into the coil for a ternary system containing inert liquid A, self‐associating liquid B and polymer C, capable of specific interactions with component B. Due to strong interactions, the assumption of random mixing is not valid for this system. In preceding work differences between experiment and prediction based on the classical Flory‐Huggins equation were formally described by the introduction of a ternary interaction term. For this particular system the ternary term may be interpreted as a consequence of the decrease in the entropy of mixing, caused by strong association of component B. On the contrary, if this component is bound to the polymer at the same time, the ternary term decreases. The equations derived in the paper lead to a reasonable fit with experimental data of the system benzene (A)/alcohol(B)/poly(methyl methacrylate)(C).

Ideals in universal algebras

In many familiar classes of algebraic structures kernels of congruence relations are uniquely specified by the inverse images q~-l(0)= {x [ q~(x)= 0} of a specified constant 0. On the one hand, q~-l(0) is nothing else but the 0-class of the kernel congruence of q~, on the other hand q~-~(0) can be axiomatized intrinsically, namely q l (0 ) is an ideal (in rings, Boolean algebras, or more generally in Heyt ing algebras), a normal subgroup, resp. normal subloop (in groups, resp. loops) or a filter (in Implicat ion algebras or Boolean algebras again, where 0 is replaced by the unit). In this paper we investigate common features of all the above structures by using a general notion of " ideal" , which makes sense in all universal algebras having a constant 0 and which specializes to the familar concepts of ideal, normal subgroup or filter in each of the algebras quoted above. In all universal algebras the 0-classes of congruence relations are easily seen to be ideals, but we shall require that conversely each ideal is the 0-class of a unique congruence relation. Such algebras, or ra ther classes of algebras with this proper ty will be called "classes with ideal determined congruences" or shortly ideal determined. In Part 1, after presenting the precise definitions, we shall show that the ideal determined varieties are characterized by a Mal 'cev condition, which turns out to be a combination of Fichtner 's condition for 0-regularity together with a ternary te rm r(x, y, z) which is a weakened form of Mal 'cev 's permutabil i ty term. From a result of Hagem ann it follows that ideal-determined varieties have modular congruence lattices, so the theory of commutators becomes readily available. In