Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

Intelligence Algorithms for Increasing Navigation Systems Accuracy

Application of neural network algorithm for increasing the accuracy of navigation systems are showing. Various navigation systems, where a couple of sensors are used in the same device in different positions and the disturbances act equally on both sensors, the trained neural network can be advantageous for increasing the accuracy of system. The neural algorithm had used for determination the interconnection between the sensors errors in two channels to avoid the unobservation of navigation system. Representation of thermal error of two- component navigation sensors by time model, which coefficients depend only on parameters of the device, its orientations relative to disturbance vector allows to predict thermal errors change, measuring the current temperature and having identified preliminary parameters of the model for the set position. These properties of thermal model are used for training the neural network and compensation the errors of navigation system in non- stationary thermal fields.

Exact Discriminant Function Design Using Some Optimization Techniques

Some aspects of design of the discriminant functions that in the best way separate points of predefined final sets are considered. The concept is introduced of the nested discriminant functions which allow to separate correctly points of any of the final sets. It is proposed to apply some methods of non-smooth optimization to solve arising extremal problems efficiently.

A PVT-Type Algorithm for Minimizing a Nonsmooth Convex Function

2000 Mathematics Subject Classification: 90C25, 68W10, 49M37.

Accurate WKB Approximation for a 1D Problem with Low Regularity

2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.

Low Volatility Options and Numerical Diffusion of Finite Difference Schemes

2000 Mathematics Subject Classification: 65M06, 65M12.

Special compositions in affinely connected spaces without a torsion

2000 Mathematics Subject Classification: 53B05, 53B99.

On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves

Here we study the integers (d, g, r) such that on a smooth projective curve of genus g there exists a rank r stable vector bundle with degree d and spanned by its global sections.

Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

Symmetric and Asymmetric Gaps in Some Fields of Formal Power Series

2000 Mathematics Subject Classification: 03E04, 12J15, 12J25.

On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness

2000 Mathematics Subject Classification: 35L15, Secondary 35L30.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.