Oscillation Theorems for Perturbed Second Order Nonlinear Differential Equations with Damping

Some oscillation criteria for solutions of a general perturbed second order ordinary differential equation with damping (r(t)x′ (t))′ + h(t)f (x)x′ (t) + ψ(t, x) = H(t, x(t), x′ (t)) with alternating coefficients are given. The results obtained improve and extend some existing results in the literature.

Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations

Oscillation criteria are given for the second order sublinear non-autonomous differential equation. (r(t) (x)x′(t))′ + q(t)g(x(t)) = (t). These criteria extends and improves earlier oscillation criteria of Kamenev, Kura, Philos and Wong. Oscillation criteria are also given for second order sublinear damped non-autonomous differential equations.

Oscillation Criteria for First Order Delay Differential Equations

2000 Mathematics Subject Classification: 34K15.

Oscillation Properties of Some Functional Fourth Order Ordinary Differential Equations

2010 Mathematics Subject Classification: 34A30, 34A40, 34C10.

Plaintext Recovery in DES-like Cryptosystems Based on S-boxes with Embedded Parity Check

We describe an approach for recovering the plaintext in block ciphers having a design structure similar to the Data Encryption Standard but with improperly constructed S-boxes. The experiments with a backtracking search algorithm performing this kind of attack against modified DES/Triple-DES in ECB mode show that the unknown plaintext can be recovered with a small amount of uncertainty and this algorithm is highly efficient both in time and memory costs for plaintext sources with relatively low entropy. Our investigations demonstrate once again that modifications resulting to S-boxes which still satisfy some design criteria may lead to very weak ciphers. ACM Computing Classification System (1998): E.3, I.2.7, I.2.8.

Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Oscillation of Nonlinear Neutral Delay Differential Equations

2000 Mathematics Subject Classification: 34K15, 34C10.

Interval Oscillation for Second Order Nonlinear Differential Equations with a Damping Term

2000 Mathematics Subject Classification: 34C10, 34C15.

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.