“…Furthermore, balanced treatment groups lead to stable statistical models. However, one of the limitations of our study is the inability to adjust for unobserved or unknown confounders. …”
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“…Overall, the cumulated amount of person-time of exposure to biological drugs approved for IMIDs provides enough statistical power to investigate weak/moderate associations of almost all individual compounds and the most relevant safety outcomes. …”
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“…Between-group analysis: The differences between TG and CG were statistically significant: in Δt (p<0.001); ΔpVO2 (p=0.012); Δ6-MWT (p<0.001). …”
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“…The discovery potential, based on simple event counting, is analysed in terms of statistical significance. A significant degradation of the discovery potential is expected due to the sizable systematic uncertainties affecting the expected amount of background feeding into the signal selection. …”
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“…NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS Inadequacy of Classical Description for Small Systems Basis of Quantum Mechanics Representation of States Dual Vectors: Bra and Ket Vectors Linear Operators Adjoint of a Linear Operator Eigenvalues and Eigenvectors of a Linear Operator Physical Interpretation Observables and Completeness Criterion Commutativity and Compatibility of Observables Position and Momentum Commutation Relations Commutation Relation and the Uncertainty ProductAppendix: Basic Concepts in Classical MechanicsREPRESENTATION THEORY Meaning of Representation How to Set up a Representation Representatives of a Linear Operator Change of Representation Coordinate Representation Replacement of Momentum Observable p by -ih d/dqIntegral Representation of Dirac Bracket A2|F|A1> The Momentum Representation Dirac Delta FunctionRelation between the Coordinate and Momentum RepresentationsEQUATIONS OF MOTIONSchrödinger Equation of Motion Schrödinger Equation in the Coordinate Representation Equation of Continuity Stationary States Time-Independent Schrödinger Equation in the Coordinate Representation Time-Independent Schrödinger Equation in the Momentum Representation Time-Independent Schrödinger Equation in Matrix Form The Heisenberg Picture The Interaction Picture Appendix: MatricesPROBLEMS OF ONE-DIMENSIONAL POTENTIAL BARRIERS Motion of a Particle across a Potential Step Passage of a Particle through a Potential Barrier of Finite Extent Tunneling of a Particle through a Potential Barrier Bound States in a One-Dimensional Square Potential Well Motion of a Particle in a Periodic PotentialBOUND STATES OF SIMPLE SYSTEMS Introduction Motion of a Particle in a Box Simple Harmonic Oscillator Operator Formulation of the Simple Harmonic Oscillator Problem Bound State of a Two-Particle System with Central Interaction Bound States of Hydrogen (or Hydrogen-Like) Atoms The Deuteron Problem Energy Levels in a Three-Dimensional Square Well: General Case Energy Levels in an Isotropic Harmonic Potential Well Appendix 1: Special FunctionsAppendix 2: Orthogonal Curvilinear Coordinate SystemsSYMMETRIES AND CONSERVATION LAWS Symmetries and Their Group Properties Symmetries in a Quantum Mechanical System Basic Symmetry Groups of the Hamiltonian and Conservation Laws Lie Groups and Their Generators Examples of Lie Group Appendix 1: Groups and RepresentationsANGULAR MOMENTUM IN QUANTUM MECHANICS Introduction Raising and Lowering Operators Matrix Representation of Angular Momentum Operators Matrix Representation of Eigenstates of Angular Momentum Coordinate Representation of Orbital Angular Momentum Operators and States General Rotation Group and Rotation Matrices Coupling of Two Angular Momenta Properties of Clebsch-Gordan Coefficients Coupling of Three Angular Momenta Coupling of Four Angular Momenta (L - S and j - j Coupling)APPROXIMATION METHODS Introduction Nondegenerate Time-Independent Perturbation Theory Time-Independent Degenerate Perturbation Theory The Zeeman Effect WKBJ Approximation Particle in a Potential Well Application of WKBJ Approximation to a-decay The Variational Method The Problem of the Hydrogen Molecule System of n Identical Particles: Symmetric and Antisymmetric States Excited States of the Helium Atom Statistical (Thomas-Fermi) Model of the Atom Hartree's Self-consistent Field Method for Multi-Electron Atoms Hartree-Fock Equations Occupation Number RepresentationQUANTUM THEORY OF SCATTERING Introduction Laboratory and Center-of-Mass (CM) Reference Frames Scattering Equation and the Scattering AmplitudePartial Waves and Phase Shifts Calculation of Phase Shift Phase Shifts for Some Simple Potential Forms Scattering due to Coulomb Potential The Integral Form of Scattering Equation Lippmann-Schwinger Equation and the Transition Operator Born Expansion Appendix: The Calculus of ResiduesTIME-DEPENDENT PERTURBATION METHODS Introduction Perturbation Constant over an Interval of Time Harmonic Perturbation: Semiclassical Theory of Radiation Einstein Coeffcients Multipole Transitions Electric Dipole Transitions in Atoms and Selection Rules Photo-Electric Effect Sudden and Adiabatic Approximations Second-Order EffectsTHE THREE-BODY PROBLEM Introduction Eyges Approach Mitra's Approach Faddeev's Approach Faddeev Equations in Momentum Representation Faddeev Equations for a Three-Body Bound System Alt, Grassberger, and Sandhas (AGS) EquationsRELATIVISTIC QUANTUM MECHANICS Introduction Dirac Equation Spin of the Electron Free Particle (Plane Wave) Solutions of Dirac Equation Dirac Equation for a Zero Mass Particle Zitterbewegung and Negative Energy Solutions Dirac Equation for an Electron in an Electromagnetic FieldInvariance of Dirac Equation Dirac Bilinear Covariants Dirac Electron in a Spherically Symmetric Potential Charge Conjugation, Parity, and Time-Reversal Invariance Appendix: Theory of Special RelativityQUANTIZATION OF RADIATION FIELD Introduction Radiation Field as a Swarm of Oscillators Quantization of Radiation Field Interaction of Matter with Quantized Radiation Field Applications Bethe's Treatment of Atomic Level Shift Due to the Self Energy of the Electron: (Lamb-Retherford Shift)Compton Scattering Appendix: Electromagnetic Field in Coulomb GaugeSECOND QUANTIZATION Introduction Classical Concept of Field Analogy of Field and Particle Mechanics Field Equations from Lagrangian DensityQuantization of a Real Scalar (KG) Field Quantization of Complex Scalar (KG) Field Dirac Field and Its Quantization Positron Operators and SpinorsInteracting Fields and the Covariant Perturbation Theory Second-Order Processes in Electrodynamics Amplitude for Compton Scattering Feynman Graphs Calculation of the Cross-Section of Compton Scattering Cross-Sections for Other Electromagnetic Processes Appendix 1: Calculus of Variation and Euler-Lagrange Equations Appendix 2: Functionals and Functional Derivatives Appendix 3: Interaction of the Electron and Radiation Fields Appendix 4: On the Convergence of Iterative Expansion of the S OperatorEPILOGUE Introduction Einstein-Podolsky-Rosen Gedanken Experiment Einstein-Podolsky-Rosen-Bohm Gedanken Experiment Theory of Hidden Variables and Bell's Inequality Clauser-Horne Form of Bell's Inequality and Its Violation in Two-Photon Correlation Experiments GENERAL REFERENCESINDEX.…”
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“…For this purpose, various electrical tests and simulations have been performed on different prototypes (1) to understand the quality of the signal transmission by means of eye-diagram analysis software and a four-ports Vector Network Analyzer; (2) to define the best configuration of the power planes for chip powering by means of the Cadence Allegro Sigrity simulation tool; (3) to define the best production strategy in terms of circuit design and choice of materials. Finally, a statistical study of the first produced Staves all around the world will give a comprehensive picture of their working parameters.…”
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“…In chapter 11, a detailed description of the statistical and systematic uncertainties is given. …”
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“…Currently there are about 30 collective that from different locations activate the device throughout the country: in 2015 they managed to accompany 2894 abortions.In this article we analyze the aid, emphasizing two central aspects of that device: the generation of links with agents of the public and private health, and the development of statistical data about women accompanied as they reflect the effectiveness of medication used to abort. …”
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“…A meta‐analysis of 16 studies indicates an overall positive, statistically significant and large effect of the interventions for skills for social inclusion with standardised mean difference (SMD) = 0.87, confidence interval (CI) = 0.57 to 1.16, k = 26, I (2) = 77%, p < 0.001). …”
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“…A nested logistic model (NLM) and a latent-class logit (LCL) model were used for statistical analysis. RESULTS: A total of 208 (response rate 62.1%) migrant participants were included. …”
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“…The random-effects model was used to compute the meta-analyses, reporting Hedges’ g effect sizes (ES) with 95% confidence intervals (95% CIs). Statistical significance was set at p ≤ 0.05. Subgroup analyses were performed (chronological age; PJT duration, frequency, number of sessions, total number of jumps; randomization). …”
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“…CONCLUSION: Severe perineal lacerations were found to be a rare complication of vaginal delivery. By using a robust statistical model, such as propensity score matching, we were able to investigate a broad range of antenatal and intrapartum risk factors, including use of epidural anesthesia, number of obstetrics examinations, and patient position at birth, which are usually underreported. …”
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“…However, even if not statistically significant, there were twice as many patients with distant relapses in the group of patients who had not IC. …”
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“…DESIGN: A systematic appraisal and statistical aggregation of primary studies. DATA SOURCES: Scopus/ELSEVIER, PubMed/MEDLINE, Clarivate Analytics’ Web of Science (i.e., Web of Science Core Collection—WoS, Korean Journal Database—KJD, Russian Science Citation Index—RSCI, SciELO Citation Index—SCIELO), and Cochrane Central Register of Controlled Trials (CENTRAL) via the Cochrane Library.The complementary searches consisted of OpenGrey, Google Scholar (first 100 returns), Networked Digital Library of Theses and Dissertations, Open Access Theses and Dissertations, DART-Europe E-theses Portal—DEEP, Opening access to UK theses—EThOS. …”
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“…A subgroup analysis based on injection sites showed that no statistical difference in efficacy between intra-articular (IA) combined with intra-osseous (IO) simultaneous PRP injections. …”
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“…Linear regression were used to correlate T1ρ relaxation times with BMI for the single dislocation, multiple dislocations, and control groups. Statistical significance was set at p < 0.05. RESULTS: Patellofemoral T1ρ relaxation times increased with BMI for healthy control subjects, but decreased with BMI following patellar dislocation. …”
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“…Data was acquired on a BD lsrFortessa flow cytometer and analyzed with FlowJo v10. Statistical analyses were performed with GraphPad Prism including parametric ANOVA (one-way or two- way), simple linear regression, Kruskal Wallis analysis of variance, Mann Whitney T-test, and parallel Principal component analyses (Eigenvalue with Monte Carlo simulation). …”
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“…A Welch’s t-test was performed for the Mini-Z and PFI data collection and determined results were statistically significant across both samples and time periods. …”
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“…All PROs at 6 month follow up visits were not statistically different between treatment groups (Table 2). …”
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“…While many baseline characteristics were found to have a statistically significant (P < 0.05) association with observation period health care costs, only 27.3% of the variation in observation period health care costs was explained by patient characteristics in the baseline period. …”
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