Search results for "Formula"

showing 10 items of 755 documents

Local Normal Forms for First-Order Logic with Applications to Games and Automata

1999

Building on work of Gaifman [Gai82] it is shown that every first-order formula is logically equivalent to a formula of the form ∃ x_1,...,x_l, \forall y, φ where φ is r-local around y, i.e. quantification in φ is restricted to elements of the universe of distance at most r from y. \par From this and related normal forms, variants of the Ehrenfeucht game for first-order and existential monadic second-order logic are developed that restrict the possible strategies for the spoiler, one of the two players. This makes proofs of the existence of a winning strategy for the duplicator, the other player, easier and can thus simplify inexpressibility proofs. \par As another application, automata mode…

General Computer ScienceLogical equivalenceautomataComputer scienceOf the formMathematical proofMonadic predicate calculusTheoretical Computer ScienceCombinatoricslocalityDeterministic automatonDiscrete Mathematics and CombinatoricsMathematicsgamesDiscrete mathematicsPredicate logiclcsh:MathematicsLocalityAtomic formulaexistential monadic second-order logiclcsh:QA1-939AutomatonFirst-order logic[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESAutomata theoryFirst-order logicDiscrete Mathematics & Theoretical Computer Science
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Excited states of the water molecule: Analysis of the valence and Rydberg character

2008

The excited states of the water molecule have been analyzed by using the extended quantum-chemical multistate CASPT2 method, namely, MS-CASPT2, in conjunction with large one-electron basis sets of atomic natural orbital type. The study includes 13 singlet and triplet excited states, both valence and 3s-, 3p-, and 3d-members of the Rydberg series converging to the lowest ionization potential and the 3s- and 3p-Rydberg members converging to the second low-lying state of the cation, 1 math. The research has been focused on the analysis of the valence or Rydberg character of the low-lying states. The computation of the 1 math state of water at different geometries indicates that it has a predom…

General Physics and AstronomyElectronssymbols.namesakeAb initio quantum chemistry methodsMoleculePhysics::Atomic PhysicsSinglet statePhysical and Theoretical Chemistry:FÍSICA::Química física [UNESCO]Valence (chemistry)ChemistryAb initio calculations ; Molecular configurations ; Orbital calculations ; Quantum chemistry ; Rydberg states ; SCF calculations ; Valency ; WaterValencyWaterRydberg statesMolecular configurationsUNESCO::FÍSICA::Química físicaOrbital calculationsExcited stateRydberg atomRydberg formulasymbolsQuantum TheorySCF calculationsAb initio calculationsIonization energyAtomic physicsQuantum chemistryAlgorithmsThe Journal of Chemical Physics
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On the fractional probabilistic Taylor's and mean value theorems

2016

In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…

Generalized Taylor’s formulaMean value theoremSurvival bounded order01 natural sciencesStochastic ordering010104 statistics & probabilityCharacterization of exponential distribution; Fractional calculus; Fractional equilibrium distribution; Generalized Taylor’s formula; Mean value theorem; Survival bounded orderFOS: MathematicsCharacterization of exponential distributionApplied mathematics0101 mathematicsMathematicsComputer Science::Information RetrievalApplied MathematicsProbability (math.PR)010102 general mathematicsProbabilistic logic60E99 26A33 26A24Fractional calculusFractional equilibrium distributionFractional calculusExponential functionDistribution (mathematics)Bounded functionMean value theorem (divided differences)Random variableAnalysisMathematics - Probability
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In Vitro Techniques

2006

Driven in part by the development of genomics, proteomics, and bioinformatics as new disciplines, there has been a tremendous resurgence of interest in physical methods to investigate macromolecular structure and function in the context of living cells. This volume in Methods in Cell Biology is devoted to biophysical techniques in vitro and their applications to cellular biology. The volume covers methods-oriented chapters on fundamental as well as cutting-edge techniques in molecular and cellular biophysics.This book is directed toward the broad audience of cell biologists, biophysicists, pharmacologists, and molecular biologists who employ classical and modern biophysical technologies or …

GeneticsIn Vitro TechniquesFda approvalGenomicsContext (language use)Full colorBiologyDrug formulationsData scienceStructure and function
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Discrete Structure Shakedown Design Ices ’95, Hawai, July 30 – August 3, 1995

1995

The minimum volume shakedown design problem was already approached by several authors with studies devoted to discrete structures (see e.g. [1]–[5]) and to continuous structures (see e.g. [6]). Except some very simple structural typologies, also the optimal shakedown design problem formulations for continuous structures need to be discretized in the application stage. In any case, the relevant optimal shakedown design problem for discrete (or discretized) structures is formulated in terms of design variables as well as behavioural variables, and consists in the search for the/a minimum volume design among all feasible designs (i.e. able to shakedown). Due to its strong non-linearity, the la…

GeographyDiscretizationMeteorologyProblem FormulationsSimple (abstract algebra)Structure (category theory)Applied mathematicsShakedown
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Pressure inactivation kinetics of Enterobacter sakazakii in infant formula milk

2007

Survival curves of Enterobacter sakazakii inactivated by high hydrostatic pressure were obtained at four pressure levels (250, 300, 350, and 400 MPa), at temperatures below 30 degrees C, in buffered peptone water (BPW; 0.3%, wt/vol) and infant formula milk (IFM; 16%, wt/vol). A linear model and four nonlinear models (Weibull, log-logistic, modified Gompertz, and Baranyi) were fitted to the data, and the performances of the models were compared. The linear regression model for the survival curves in BPW and IFM at 250 MPa has fitted regression coefficient (R2) values of 0.940 to 0.700, respectively, and root mean square errors (RMSEs) of 0.770 to 0.370. For the other pressure levels, the lin…

Gompertz functionHydrostatic pressureAnalytical chemistryColony Count MicrobialFood ContaminationMicrobiologyModels BiologicalMicrobiologyRoot mean squareCronobacter sakazakiiLinear regressionHydrostatic PressureAnimalsHumansModels StatisticalbiologyChemistryLinear modelInfant NewbornInfantEnterobacterbiology.organism_classificationInfant FormulaKineticsMilkInfant formulaConsumer Product SafetyFood MicrobiologyInfant FoodNonlinear regressionFood Science
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A rational runoff coefficient for a revisited rational formula

2019

The Rational Formula (RF) is probably the most frequently applied equation in practical hydrology to compute the peak discharge, due to its simplicity and effective compromise between theory and data availability. Thus, after more than a century, the estimation of peak discharge through the RF is still an important and challenging issue in hydrology. The RF assumes response linearity and sometimes assumes that the return period does not depend on the runoff coefficient and neglects the time to ponding and the antecedent moisture condition. Moreover, the RF requires the critical duration of rainfall and the runoff coefficient to be estimated, both of which are highly controversial. This pape…

Green-Ampt modelmedia_common.quotation_subject0208 environmental biotechnologyhydrological response02 engineering and technology020801 environmental engineeringRunoff coefficientHydrology (agriculture)rational formulahillslope scaleSettore AGR/08 - Idraulica Agraria E Sistemazioni Idraulico-ForestaliApplied mathematicskinematic wave modelSimplicityrunoff coefficientWater Science and Technologymedia_commonMathematicsHydrological Sciences Journal
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Safety and efficacy of a probiotic-containing infant formula supplemented with 2'-fucosyllactose: a double-blind randomized controlled trial

2022

Abstract Background Human milk oligosaccharides (HMOs) have important and diverse biological functions in early life. This study tested the safety and efficacy of a starter infant formula containing Limosilactobacillus (L.) reuteri DSM 17938 and supplemented with 2’-fucosyllactose (2’FL). Methods Healthy infants < 14 days old (n = 289) were randomly assigned to a bovine milk-based formula containing L. reuteri DSM 17938 at 1 × 107 CFU/g (control group; CG) or the same formula with added 1.0 g/L 2’FL (experimental group; EG) until 6 months of age. A non-randomized breastfed group served as reference (BF; n = 60). The primary endpoint was weight gain through 4 months of age in the formula-…

Gut microbiomeNutrition and DieteticsMilk HumanProbioticsgrowthHuman milk oligosaccharidesMedicine (miscellaneous)InfantOligosaccharidesgut microbiomeinfant formulaGrowth2’fucosyllactose2’fucosyllactose Growth Gut microbiome Human milk oligosaccharides Infant formula2'fucosyllactoseFecesDouble-Blind MethodInfant formulaHumansPediatrics Perinatology and Child HealthTrisaccharidesPhylogeny
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Structure and physical properties of [mu-tris(1,4-bis(tetrazol-1-yl)butane-N4,N4 ')iron(II)] bis(hexafluorophosphate), a new Fe(II) spin-crossover co…

2004

[mu-Tris(1,4-bis(tetrazol-1-yl)butane-N4,N4')iron(II)] bis(hexafluorophosphate), [Fe(btzb)(3)](PF6)(2), crystallizes in a three-dimensional 3-fold interlocked structure featuring a sharp two-step spin-crossover behavior. The spin conversion takes place between 164 and 182 K showing a discontinuity at about T-1/2 = 174 K and a hysteresis of about 4 K between T-1/2 and the low-spin state. The spin transition has been independently followed by magnetic susceptibility measurements, Fe-57-Mossbauer spectroscopy, and variable temperature far and midrange FIR spectroscopy. The title compound crystallizes in the trigonal space group P (3) over bar (No. 147) with a unit cell content of one formula u…

HALOGENATED ETHYLTETRAZOLESIRON(II)StereochemistrySpin transitionCrystal structureMagnetic susceptibilityTHERMAL HYSTERESISInorganic ChemistryBond lengthchemistry.chemical_compoundCrystallographyLattice constantchemistryMOLECULAR-INTERACTIONSSpin crossoverMAGNETIC-PROPERTIESFormula unitHexafluorophosphateTHEORETICAL DESCRIPTIONMOSSBAUERPHASE-TRANSITIONCOMPLEXESPhysical and Theoretical ChemistryELASTIC INTERACTION
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Paediatric oral formulations: comparison of two extemporaneously compounded suspensions from tacrolimus capsules

2011

Study objectives: The objective of this study was to determine the stability of tacrolimus in extemporaneously compounded liquid formulations. Methods: Two sets of liquid formulations were prepared using two different vehicles: one set in sterile water and in simple syrup (1:1) and one set using equal volumes of commercially available suspending agent (Ora-Plus) and simple syrup. The concentration of tacrolimus in each formulation was 0.5 mg/mL. The preparations containing Ora-Plus were stored at 25°C, the formulations that were prepared with sterile water and simple syrup were stored under refrigeration at 4°C. Results: Samples were collected at regular time intervals over a period of 56 d…

HPLC liquid formulation Ora-Plus stability tacrolimusSettore CHIM/08 - Chimica Farmaceutica
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