Self-Learning Fuzzy Spiking Neural Network as a Nonlinear Pulse-Position Threshold Detection Dynamic System Based on Second-Order Critically Damped Response Units

Architecture and learning algorithm of self-learning spiking neural network in fuzzy clustering task are outlined. Fuzzy receptive neurons for pulse-position transformation of input data are considered. It is proposed to treat a spiking neural network in terms of classical automatic control theory apparatus based on the Laplace transform. It is shown that synapse functioning can be easily modeled by a second order damped response unit. Spiking neuron soma is presented as a threshold detection unit. Thus, the proposed fuzzy spiking neural network is an analog-digital nonlinear pulse-position dynamic system. It is demonstrated how fuzzy probabilistic and possibilistic clustering approaches can be implemented on the base of the presented spiking neural network.

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 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.

Optimal Control of a Second Order Parabolic Heat Equation

In this paper, we are concerned with the optimal control boundary control of a second order parabolic heat equation. Using the results in [Evtushenko, 1997] and spatial central finite difference with diagonally implicit Runge-Kutta method (DIRK) is applied to solve the parabolic heat equation. The conjugate gradient method (CGM) is applied to solve the distributed control problem. Numerical results are reported.

Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems

2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30.

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

On a Second Order Condition for Max-Semistable Laws

2000 Mathematics Subject Classification: 62G32, 62G20.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

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

2000 Mathematics Subject Classification: 34C10, 34C15.

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.

Methods for Solving Necessary Equivalences

Nonmonotonic Logics such as Autoepistemic Logic, Reflective Logic, and Default Logic, are usually defined in terms of set-theoretic fixed-point equations defined over deductively closed sets of sentences of First Order Logic. Such systems may also be represented as necessary equivalences in a Modal Logic stronger than S5 with the added advantage that such representations may be generalized to allow quantified variables crossing modal scopes resulting in a Quantified Autoepistemic Logic, a Quantified Autoepistemic Kernel, a Quantified Reflective Logic, and a Quantified Default Logic. Quantifiers in all these generalizations obey all the normal laws of logic including both the Barcan formula and its converse. Herein, we address the problem of solving some necessary equivalences containing universal quantifiers over modal scopes. Solutions obtained by these methods are then compared to related results obtained in the literature by Circumscription in Second Order Logic since the disjunction of all the solutions of a necessary equivalence containing just normal defaults in these Quantified Logics, is equivalent to that system.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90