“…A statistically significant difference was observed between the 2 groups in terms of plaque, (p=0.036), calculus (p=0.001) and gingival indices (p<0.001). …”
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“…The most prevalent oral conditions were plaque and surface calculus found in 66.0% of the respondents respectively. …”
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“…The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. …”
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“…THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATIONS INTRODUCTION SYMBOLIC METHODS LAGRANGE'S AND SEPARATION-OF-VARIABLES METHODS LAPLACE'S METHOD PARTICULAR SOLUTIONS SIMULTANEOUS EQUATIONS WITH CONSTANT COEFFICIENTS NONLINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS RICCATI EQUATIONS CLAIRAUT'S EQUATION NONLINEAR TRANSFORMATIONS, MISCELLANEOUS FORMS PARTIAL DIFFERENCE EQUATIONS APPLICATIONS INTRODUCTION MATHEMATICS PERTURBATION TECHNIQUES STABILITY OF FIXED POINTS THE LOGISTIC EQUATION NUMERICAL INTEGRATION OF DIFFERENTIAL EQUATIONS PHYSICAL SYSTEMS ECONOMICS WARFAREBIOLOGICAL SCIENCES SOCIAL SCIENCES MISCELLANEOUS APPLICATIONS ADVANCED TOPICSINTRODUCTION GENERALIZED METHOD OF SEPARATION OF VARIABLESCAUCHY-EULER EQUATION GAMMA AND BETA FUNCTIONS LAMBERT-W FUNCTION THE SYMBOLIC CALCULUS MIXED DIFFERENTIAL AND DIFFERENCE EQUATIONSEULER POLYNOMIALS FUNCTIONAL EQUATIONSFUNCTIONAL EQUATION f(x)2 + g(x)2 = 1 EXACT DISCRETIZATIONS OF DIFFERENTIAL EQUATIONSADVANCED APPLICATIONS FINITE DIFFERENCE SCHEME FOR THE RELUGA x - y - z MODEL DISCRETE-TIME FRACTIONAL POWER DAMPED OSCILLATOREXACT FINITE DIFFERENCE REPRESENTATION OF THE MICHAELIS-MENTON EQUATION DISCRETE DUFFING EQUATION DISCRETE HAMILTONIAN SYSTEMS ASYMPTOTICS OF SCHRODINGER-TYPE DIFFERENCE EQUATIONS BLACK-SCHOLES EQUATIONS Appendix: Useful Mathematical Relations Bibliography Index.…”
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“…Bleeding on probing (BOP), calculus deposition and probing pocket depth (PPD) were investigated. …”
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“…RESULTS: The samples of the study showed high levels of dental plaque, dental calculus and BOP. The final multivariate model showed that age (p=0.000), gender (p=0.016) and presence of calculus (p=0.000) were associated with the mean clinical attachment loss. …”
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“…We explore the use of the Qualitative Trajectory Calculus (QTC), a spatiotemporal qualitative calculus describing the relative movement between objects, for spatial movement pattern recognition of players movements in soccer. …”
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“…We can now examine these communities by sequencing ancient DNA preserved within calcified dental plaque (calculus), providing insights into the origins of disease and their links to human history. …”
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“…The next generation of life science professionals will require far more quantitative skills than prior generations. Calculus is important for understanding dynamical systems in biology and, therefore, is often a required course for life science students. …”
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“…All these data supply various interesting food for thought and expand the knowledge about the potential of dental calculus in archaeological and archaeobotanical fields with a special focus on palaeoecology.…”
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“…Urinary calculus is more commonly known in infants, and the urinary bladder is the most common location in the lower urinary tract for stone formation. …”
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“…The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions…”
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“…The second part presents the results of recent research by the author on martingale theory and stochastic calculus for two-parameter processes. Both the results and the methods of these two chapters are almost entirely new, and are of particular interest. …”
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“…Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. …”
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“…Its main objective is an extension of the classical variational calculus on Euclidean spaces to (topologically nontrivial) finite-dimensional smooth manifolds; to this purpose the methods of global analysis of differential forms are used. …”
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