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HalfLinear Dynamic Equations
"... Abstract. We survey halflinear dynamic equations on time scales. These contain the wellknown halflinear differential and halflinear difference equations as special cases, but also other kinds of halflinear equations. Special cases of halflinear equations are the wellstudied linear equations o ..."
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of second order. We discuss existence and uniqueness of solutions of corresponding initial value problems and, using a Picone identity, derive a Reid roundabout theorem that gives conditions equivalent to disconjugacy of halflinear dynamic equations, among them solvability of an associated Riccati equation
An Oscillatory HalfLinear Differential Equation
, 1997
"... . A secondorder halflinear ordinary differential equation of the type (1) (jy 0 j ff\Gamma1 y 0 ) 0 + ffq(t)jyj ff\Gamma1 y = 0 is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution of ..."
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. A secondorder halflinear ordinary differential equation of the type (1) (jy 0 j ff\Gamma1 y 0 ) 0 + ffq(t)jyj ff\Gamma1 y = 0 is considered on an unbounded interval. A simple oscillation condition for (1) is given in such a way that an explicit asymptotic formula for the distribution
HALF–LINEAR DISCRETE OSCILLATION THEORY
"... ABSTRACT. Oscillatory properties of the second order halflinear difference equation ∆(rk∆yk  α−2 ∆yk) + pkyk+1  α−2 yk+1 = 0, where α> 1, are investigated. A particular attention is devoted to the connection with oscillation theory of its continuous counterpart, half–linear differential equa ..."
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ABSTRACT. Oscillatory properties of the second order halflinear difference equation ∆(rk∆yk  α−2 ∆yk) + pkyk+1  α−2 yk+1 = 0, where α> 1, are investigated. A particular attention is devoted to the connection with oscillation theory of its continuous counterpart, half–linear differential
CONJUGACY AND PRINCIPAL SOLUTION OF GENERALIZED HALFLINEAR SECOND ORDER DIFFERENTIAL EQUATIONS
"... Abstract. We study the generalized halflinear second order differential equation and the associated Riccati type differential equation. We introduce the concepts of minimal and principal solutions of these equations and using these concepts we prove a new conjugacy criterion for the generalized hal ..."
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Abstract. We study the generalized halflinear second order differential equation and the associated Riccati type differential equation. We introduce the concepts of minimal and principal solutions of these equations and using these concepts we prove a new conjugacy criterion for the generalized
A Picone type identity for second order halflinear dierential equations
 Acta Math. Univ. Comenianae
, 1999
"... Abstract. In the paper a Piconetype identity for halflinear differential equations of second order is derived and Sturmian theory for both forced and unforced halflinear and quasilinear equations based on this identity is developed. 1. ..."
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Abstract. In the paper a Piconetype identity for halflinear differential equations of second order is derived and Sturmian theory for both forced and unforced halflinear and quasilinear equations based on this identity is developed. 1.
Asymptotic Confidence Intervals for Indirect Effects in Structural EQUATION MODELS
 IN SOCIOLOGICAL METHODOLOGY
, 1982
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Oscillation criteria for sublinear halflinear delay dynamic equations on time scales
 Int. J. Difference Equ
"... This paper is concerned with oscillation of the secondorder halflinear delay dynamic equation (r(t)(x∆)γ) ∆ + p(t)xγ(τ(t)) = 0, on a time scale T where 0 < γ ≤ 1 is the quotient of odd positive integers, p: T → [0,∞), and τ: T → T are positive rdcontinuous functions, r(t) is a positive and (d ..."
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Cited by 7 (5 self)
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This paper is concerned with oscillation of the secondorder halflinear delay dynamic equation (r(t)(x∆)γ) ∆ + p(t)xγ(τ(t)) = 0, on a time scale T where 0 < γ ≤ 1 is the quotient of odd positive integers, p: T → [0,∞), and τ: T → T are positive rdcontinuous functions, r(t) is a positive
OSCILLATION OF SECOND ORDER HALFLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING
"... Abstract. This paper is concerned with a class of second order halflinear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing result ..."
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Abstract. This paper is concerned with a class of second order halflinear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing
Differential privacy . . .
, 2009
"... We show by means of several examples that robust statistical estimators present an excellent starting point for differentially private estimators. Our algorithms use a new paradigm for differentially private mechanisms, which we call ProposeTestRelease (PTR), and for which we give a formal definit ..."
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Cited by 629 (10 self)
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We show by means of several examples that robust statistical estimators present an excellent starting point for differentially private estimators. Our algorithms use a new paradigm for differentially private mechanisms, which we call ProposeTestRelease (PTR), and for which we give a formal
Results 1  10
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