Search results for "NUMBERS"

showing 10 items of 128 documents

Extended Natural Numbers and Counters

2020

Summary This article introduces extended natural numbers, i.e. the set ℕ ∪ {+∞}, in Mizar [4], [3] and formalizes a way to list a cardinal numbers of cardinals. Both concepts have applications in graph theory.

Applied Mathematics03e10 68v20Mathematics::General Topology020207 software engineeringNatural number0102 computer and information sciences02 engineering and technologysequence01 natural sciencesCombinatoricsComputational MathematicsMathematics::Logic010201 computation theory & mathematicscardinal0202 electrical engineering electronic engineering information engineeringextended natural numbersQA1-939MathematicsMathematicsSequence (medicine)MathematicsofComputing_DISCRETEMATHEMATICSFormalized Mathematics
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Cluster Analysis Tailored to Structure Change of Tropical Cyclones Using a Very Large Number of Trajectories

2020

AbstractMajor airstreams in tropical cyclones (TCs) are rarely described from a Lagrangian perspective. Such a perspective, however, is required to account for asymmetries and time dependence of the TC circulation. We present a procedure that identifies main airstreams in TCs based on trajectory clustering. The procedure takes into account the TC’s large degree of inherent symmetry and is suitable for a very large number of trajectories . A large number of trajectories may be needed to resolve both the TC’s inner-core convection as well as the larger-scale environment. We define similarity of trajectories based on their shape in a storm-relative reference frame, rather than on proximity in …

Atmospheric Science010504 meteorology & atmospheric sciencesClimatologyCluster (physics)Structure (category theory)Large numbers010501 environmental sciencesTropical cyclone01 natural sciencesGeology0105 earth and related environmental sciencesMonthly Weather Review
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Groups acting freely on Calabi-Yau threefolds embedded in a product of del Pezzo surfaces

2011

In this paper, we investigate quotients of Calabi-Yau manifolds $Y$ embedded in Fano varieties $X$, which are products of two del Pezzo surfaces — with respect to groups $G$ that act freely on $Y$. In particular, we revisit some known examples and we obtain some new Calabi-Yau varieties with small Hodge numbers. The groups $G$ are subgroups of the automorphism groups of $X$, which is described in terms of the automorphism group of the two del Pezzo surfaces.

Automorphism groupPure mathematicsGeneral MathematicsGeneral Physics and AstronomyFOS: Physical sciencesFano planeMathematical Physics (math-ph)AutomorphismMathematics - Algebraic GeometryMathematics::Algebraic GeometryProduct (mathematics)FOS: MathematicsCalabi–Yau manifolddel pezzo calabi yauSettore MAT/03 - GeometriaMathematics::Differential GeometryGrupo actions Calabi-Yau threefolds hodge numbersAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryQuotientMathematical PhysicsMathematics
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Splittings of Toric Ideals

2019

Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition for this splitting in terms of the integer matrix that defines $I$. When $I = I_G$ is the toric ideal of a finite simple graph $G$, we give additional splittings of $I_G$ related to subgraphs of $G$. When there exists a splitting $I = I_1+I_2$ of the toric ideal, we show that in some cases we can describe the (multi-)graded Betti numbers of $I$ in terms of the (multi-)graded Betti numbers of $I_1$ and $I_2$.

Binomial (polynomial)Betti numberPrime idealExistential quantificationCommutative Algebra (math.AC)01 natural sciencesCombinatoricsInteger matrixMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsGraded Betti numbers; Graphs; Toric idealsMathematics - Combinatorics0101 mathematicsMathematics::Symplectic GeometryMathematicsAlgebra and Number TheorySimple graphIdeal (set theory)Mathematics::Commutative AlgebraGraded Betti numbers Graphs Toric ideals010102 general mathematicsMathematics::Rings and Algebras16. Peace & justiceMathematics - Commutative AlgebraSettore MAT/02 - AlgebraToric ideals13D02 13P10 14M25 05E40Settore MAT/03 - Geometria010307 mathematical physicsCombinatorics (math.CO)Graded Betti numbersGraphs
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Project Scheduling Methods Based on Theory of Ordered Fuzzy Numbers

2020

In this the paper we present new methods, called OFCPM, OFPERT, for estimating a project completion time in the situation when activity duration times in the project are given in the form of Ordered Fuzzy Numbers OFNs. Extended Critical Path Method and Project Evaluation and Review Technique have been developed as new methods dedicated to project scheduling, preserving its basic concept. Ordered fuzzy numbers are used to project scheduling under uncertainty. The duration time of each project activity is estimated by experts (experts views of the activity duration time) based on their experience. These new methods will be verify on some examples. The comparison of our fuzzy approaches to exi…

CPMPERTOrdered Fuzzy NumbersProject Scheduling
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Escape of Supercritical-CO2 Fluids Trapped in Calcite Nano-metric Pores

2019

Flow of supercritical CO2-bearing fluids through a rock is a fundamental phenomenon which acts upon a great many geological processes ranging from seismic activity to formation of ore deposits. Atomic Force Microscopy scanning experiments allowed us to infer movement of supercritical CO2-bearing fluids through calcite crystals and relate it to natural decrepitation of nanoscale fluid inclusions. Calculated velocities exceed the rate of diffusion predicated via current vacancy models by several orders of magnitude implying that CO2-rich fluid movement through micro and nano-pore space may presently be greatly underestimated.

Calcitelcsh:GE1-350Materials science010504 meteorology & atmospheric sciences[SDU.STU]Sciences of the Universe [physics]/Earth SciencesOrders of magnitude (numbers)010502 geochemistry & geophysics01 natural sciencesSupercritical fluidDecrepitationchemistry.chemical_compoundchemistryChemical physicsVacancy defectNano-Fluid inclusionsCO2Current (fluid)lcsh:Environmental sciences0105 earth and related environmental sciences[SDU.STU.MI]Sciences of the Universe [physics]/Earth Sciences/MineralogyE3S Web of Conferences
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A True Extension of the Markov Inequality to Negative Random Variables

2020

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for the probability that an variable differs from its expectation. However, the Markov inequality has one main flaw: its validity is limited to nonnegative random variables. In the very short note, we propose an extension of the Markov inequality to any non specified random variable. This result is completely new.

Chebyshev's inequalityLaw of large numbersComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONMarkov's inequalityMathematicsofComputing_NUMERICALANALYSISApplied mathematicsExtension (predicate logic)Random variableUpper and lower boundsMathematicsVariable (mathematics)SSRN Electronic Journal
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Do Individual Effects Reflect Quantitative or Qualitative Differences in Cognition?

2021

Rouder and Haaf (2020) posed the important question if there are some individuals whose behavior is not in accordance with well-established experimental effects and whether these individual differences are quantitative or qualitative in nature. In our commentary, we discuss the distinction between quantitative and qualitative individual differences and between individual and average causal effects and come to the conclusion that this is not a new question, but in fact one that has already been discussed by Gordon W. Allport (1937) and Donald B. Rubin (1974, 1978). Moreover, we critically examine their proposed rule of thumb to collect about 100 trials per experimental condition to reliably …

Consciousness. CognitionElementary cognitive taskmedia_common.quotation_subjectCausal effectExperimental and Cognitive PsychologyCognitioncognitive tasksMeasure (mathematics)Rule of thumbtrial numbersCommentaryFunction (engineering)Psychologyindividual differencesindividual differences; cognitive tasks; trial numbersBF309-499Cognitive psychologymedia_commonJournal of Cognition
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Intercomparing different devices for the investigation of ice nucleating particles using Snomax<sup>®</sup> as test subst…

2015

Abstract. Seven different instruments and measurement methods were used to examine the immersion freezing of bacterial ice nuclei from Snomax® (hereafter Snomax), a product containing ice-active protein complexes from non-viable Pseudomonas syringae bacteria. The experimental conditions were kept as similar as possible for the different measurements. Of the participating instruments, some examined droplets which had been made from suspensions directly, and the others examined droplets activated on previously generated Snomax particles, with particle diameters of mostly a few hundred nanometers and up to a few micrometers in some cases. Data were obtained in the temperature range from −2 to …

Contact angleAtmospheric ScienceRange (particle radiation)CrystallographyChemistrySlow coolingIce nucleusAnalytical chemistryParticleNanometreOrders of magnitude (numbers)Atmospheric temperature rangeAtmospheric Chemistry and Physics
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<title>Heavy-ion induced damage and reduction of dislocation mobility in LiF single crystals</title>

2006

Ion-induced reduction of dislocation mobility in LiF crystals irradiated with swift heavy (U) and light (Ni) ions of a specific energy of 11 MeV per nucleon at fluences between 106 and 1011 ions/cm2 was studied. The arm length of dislocation rosettes produced by indentation on (100) irradiated surface was measured. It has been found that in the case of heavy ions the threshold fluence (106 ions/cm2) for impeding of dislocation arms is about 3 orders of magnitude lower than that for light ions. The results indicate that ion-induced defect aggregates play the dominating role in the impeding of dislocations. Heavy ions, which produce defect aggregates in the track core, cause also a stronger e…

CrystallographyMaterials sciencePhysics::Plasma PhysicsRadiation damageSurface modificationIrradiationOrders of magnitude (numbers)DislocationLaser-induced fluorescenceFluenceMolecular physicsIonSPIE Proceedings
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