“…We listed the fundamental results of the fractional calculus for the analysis of our model. The model is then analyzed for the basic properties, and the existence and uniqueness of the proposed breast cancer system are investigated through fixed point theory. …”
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“…Making a decision needs a “cost-benefits calculus,” but the utility value of study abroad was positioned behind attainment value and identified motivation. …”
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“…We additionally observe that the most likely configurations for vorticity and strain spontaneously break their rotational symmetry for extremely high observable values. Instanton calculus and large deviation theory allow us to show that these maximum likelihood realizations determine the tail probabilities of the observed quantities. …”
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“…Gingival enlargement may be a result of multifactorial etiology which includes local factors such as calculus, food lodgement, overhanging restorations, and overextended dentures as well as systemic conditions such as hormonal disturbances and blood dyscrasias. …”
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“…On evaluation, she had azotemia, glycosuria, proteinuria, normal anion gap metabolic acidosis, multiple renal stones, and a proximal ureteric calculus causing right-sided hydroureteronephrosis. …”
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“…Without shortages, the necessary and sufficient conditions for optimality of this model are characterized through a theorem and lemmas while a solution methodology based on differential calculus is adopted. This paper determines the best replenishment cycle length corresponding to the optimal total variable cost and production quantity of imperfect production industry. …”
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“…We extend the Rockland criterion to a pseudodifferential calculus on filtered manifolds, construct a parametrix and describe its precise analytic structure. …”
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“…At present, percutaneous nephrolithotomy has become an option for hospitals increasingly to treat calculus. However, due to the certain risk of percutaneous nephrolithotomy, it may lead to postoperative complications. …”
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“…Acute appendicitis was successfully treated with cefmetazole, and the calculus was eliminated after adequate fluid loading. …”
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“…The vertical limb and half of the horizontal limb of the copper-T were retrieved from the outer wall of the urinary bladder laparoscopically, and the intravesical part of the horizontal limb along with the calculus was retrieved per urethra.…”
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“…RESULTS: The body was determined to be that of an adult male, who showed some pathological changes such as dental calculus and what is suspected to be hallux valgus. …”
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“…In recent times, fractional calculus has gained popularity in various types of engineering applications. …”
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“…In this study, we model the nanoparticle geometry in a Finite Element Model calculus environment to calculate the effects that occur as a response to placing it in an optical, electromagnetic field, and also a model of the experimental procedure to measure the temperature rise while irradiating a suspension of nanoparticles. (2) Methods: Finite Element Method numerical models using the COMSOL interface for geometry and mesh generation and iterative solving discretized Maxwell’s equations; (3) Results: Absorption and scattering cross-section spectrums were obtained for NanoRods and NanoStars, also varying their geometry as a parameter, along with electric field enhancement in their surroundings; temperature curves were calculated and measured as an outcome of the irradiation of different concentration suspensions; (4) Conclusions: The results obtained are comparable with the bibliography and experimental measurements.…”
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“…We introduce a novel discretization technique for both elliptic and parabolic fractional diffusion problems based on double exponential quadrature formulas and the Riesz–Dunford functional calculus. Compared to related schemes, the new method provides faster convergence with fewer parameters that need to be adjusted to the problem. …”
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“…Introduction: Probability, Statistics, and ScienceReality, Nature, Science, and ModelsStatistical Processes: Nature, Design and Measurement, and DataModelsDeterministic ModelsVariabilityParametersPurely Probabilistic Statistical ModelsStatistical Models with Both Deterministic and Probabilistic ComponentsStatistical InferenceGood and Bad ModelsUses of Probability ModelsRandom Variables and Their Probability DistributionsIntroductionTypes of Random Variables: Nominal, Ordinal, and ContinuousDiscrete Probability Distribution FunctionsContinuous Probability Distribution FunctionsSome Calculus-Derivatives and Least SquaresMore Calculus-Integrals and Cumulative Distribution FunctionsProbability Calculation and SimulationIntroductionAnalytic Calculations, Discrete and Continuous CasesSimulation-Based ApproximationGenerating Random NumbersIdentifying DistributionsIntroductionIdentifying Distributions from Theory AloneUsing Data: Estimating Distributions via the HistogramQuantiles: Theoretical and Data-Based EstimatesUsing Data: Comparing Distributions via the Quantile-Quantile PlotEffect of Randomness on Histograms and q-q PlotsConditional Distributions and IndependenceIntroductionConditional Discrete DistributionsEstimating Conditional Discrete DistributionsConditional Continuous DistributionsEstimating Conditional Continuous DistributionsIndependenceMarginal Distributions, Joint Distributions, Independence, and Bayes' TheoremIntroductionJoint and Marginal DistributionsEstimating and Visualizing Joint DistributionsConditional Distributions from Joint DistributionsJoint Distributions When Variables Are IndependentBayes' TheoremSampling from Populations and ProcessesIntroductionSampling from PopulationsCritique of the Population Interpretation of Probability ModelsThe Process Model versus the Population ModelIndependent and Identically Distributed Random Variables and Other Models Checking the iid AssumptionExpected Value and the Law of Large NumbersIntroductionDiscrete CaseContinuous CaseLaw of Large NumbersLaw of Large Numbers for the Bernoulli DistributionKeeping the Terminology Straight: Mean, Average, Sample Mean, Sample Average, and Expected ValueBootstrap Distribution and the Plug-In PrincipleFunctions of Random Variables: Their Distributions and Expected ValuesIntroductionDistributions of Functions: The Discrete CaseDistributions of Functions: The Continuous CaseExpected Values of Functions and the Law of the Unconscious StatisticianLinearity and Additivity PropertiesNonlinear Functions and Jensen's InequalityVarianceStandard Deviation, Mean Absolute Deviation, and Chebyshev's InequalityLinearity Property of VarianceSkewness and KurtosisDistributions of TotalsIntroductionAdditivity Property of VarianceCovariance and CorrelationCentral Limit TheoremEstimation: Unbiasedness, Consistency, and EfficiencyIntroductionBiased and Unbiased EstimatorsBias of the Plug-In Estimator of VarianceRemoving the Bias of the Plug-In Estimator of VarianceThe Joke Is on Us: The Standard Deviation Estimator Is Biased after AllConsistency of EstimatorsEfficiency of EstimatorsLikelihood Function and Maximum Likelihood EstimatesIntroductionLikelihood FunctionMaximum Likelihood EstimatesWald Standard ErrorBayesian StatisticsIntroduction: Play a Game with Hans!…”
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“…The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. …”
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“…Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics.* Serves as an introductory text on the development and application of mathematical models * Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems* Offers more than 360 problems, providing ample opportunities for practice * Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences* Uses straightforward language and explanations that make modeling easy to understand and applyNew to this Edition:* A more systematic approach to mathematical modeling, outlining ten specific principles* Expanded and reorganized chapters that flow in an increasing level of complexity* Several new problems and updated applications* Expanded figure captions that provide more information* Improved accessibility and flexibility for teaching…”
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“…The work assumes a modest understanding of basic statistics and calculus. Topics and Features: Introduces the burgeoning science of collectives and its practical applications in a single useful volume Combines approaches from known researchers in the physics, economics, game theory, biology, and artificial intelligence (A.I.) communities Analyzes the role of information transmission in collectives, such as in the minority game, specific game theory scenarios, and computational ecologies Presents a broad view of state-of-the-art techniques and developments in the field Describes the benefits and promise of collectives-based design of systems, and explores recent challenges faced by researchers Highlights the interdisciplinary value to studying and using collectives Provides a comprehensive subject index and chapter-ending bibliographies With an accessible style that integrates key theoretical principles with applications in real-world scenarios, this unique monograph surveys the latest research on the dynamics of collectives, their A.I.…”
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