Serdica Mathematical Journal

Volume 42, Number 2, 2016

C O N T E N T S

A B S T R A C T S

DIFFÉOMORPHISMES DE CONTACT SUR T³
Saad Aggoun saad.aggoun@yahoo.fr

2010 Mathematics Subject Classification: 37J55, 53D10, 53D17, 53D35.
Key words: Forme de contact, champ de Reeb, crochet de Poisson, automorphisme infinitésimal.

In this paper we will determine all the diffeomorphisms F on the torus T³ that leave the contact form ω_n=cos nθ₃dθ₁+sin nθ₃dθ₂ (n∈N^*) invariant (F^*ω_n=ω_n).

THE MAXIMUM PRINCIPLE IN TIME-INCONSISTENT LQ EQUILIBRIUM CONTROL PROBLEM FOR JUMP DIFFUSIONS
Ishak Alia ishak.alia@hotmail.com,
Farid Chighoub f.chighoub@univ-biskra.dz, chighoub_farid@yahoo.fr,
Ayesha Sohail asohail@ciitlahore.edu.pk

2010 Mathematics Subject Classification: 93E20, 60H30, 93E99, 60H10.
Key words: stochastic maximum principle, time inconsistency, linear quadratic control problem, equilibrium control, variational inequality.

In this paper, we discuss a class of stochastic linear quadratic dynamic decision problems of a general time-inconsistent type, in the sense that, it does not satisfy the Bellman optimality principle. More precisely, the dependence of the running and the terminal costs in the objective functional on some general discounting coefficients, as well as on some quadratic terms of the conditional expectation of the state process, makes the problem time-inconsistent. Open-loop Nash equilibrium controls are then constructed instead of optimal controls, this has been accomplished through the stochastic maximum principle approach that includes a flow of forward-backward stochastic differential equations under a maximum condition. Then by decoupling the flow of the adjoin process, we derive an explicit representation of the equilibrium strategies in feedback form. As an application, we study some concrete examples. We emphasize that; this method can provide the necessary and sufficient conditions to characterize the equilibrium strategies. While most existing results which are based on the dynamic programming principle and the extended HJB equation can create only the sufficient condition to characterize the equilibrium strategies.

RADICAL TRANSVERSAL SCREEN PSEUDO-SLANT LIGHTLIKE SUBMANIFOLDS OF INDEFINITE SASAKIAN MANIFOLDS
S. S. Shukla ssshukla_au@rediffmail.com,
Akhilesh Yadav akhilesh_mathau@rediffmail.com

2010 Mathematics Subject Classification: 53C15, 53C40, 53C50.
Key words: semi-Riemannian manifold, degenerate metric, radical distribution, screen distribution, screen transversal vector bundle, lightlike transversal vector bundle, Gauss and Weingarten formulae.

In this paper, we introduce the notion of radical transversal screen pseudo-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D₁, D₂ and RadTM on radical transversal screen pseudo-slant lightlike submanifolds of an indefinite Sasakian manifold, have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

ASYMPTOTIC BEHAVIOR OF THIRD-ORDER NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS
E. M. Elabbasy emelabbasy@mans.edu.eg,
O. Moaaz o_moaaz@mans.edu.eg

2010 Mathematics Subject Classification: 34K11, 34K15.
Key words: asymptotic behavior, third order, delay differential equations.

This work discusses asymptotic behavior of solutions of class of third-order non-linear delay differential equation with middle term. Our results in this paper extend and improve some the previous results, the sense that the results do not require delay function (g_i(t)) with monotonicity. As well, by using Riccati transformation technique, we establish some new oscillation criteria for third-order delay differential equation. Examples given in the study to clarify the new results.

COEFFICIENT BOUNDS FOR TWO NEW SUBCLASSES OF~M-FOLD SYMMETRIC BI-UNIVALENT FUNCTIONS
Şahsene Altιnkaya sahsene@uludag.edu.tr,
Sibel Yalçιn syalcin@uludag.edu.tr

2010 Mathematics Subject Classification: 30C45, 30C50.
Key words: analytic functions, $m$-fold symmetric bi-univalent functions, Coefficient bounds.

In this paper, we consider two new subclasses N^μ_{Σm(α, λ)} and N^μ_{Σm(β, λ)} of Σ_m consisting of analytic and m-fold symmetric bi-univalent functions in the open unit disk U. Furthermore, we establish bounds for the coefficients for these subclasses and several related classes are also considered and connections to earlier known results are made.

R CONTROL CHART FOR POSITIVELY SKEWED DISTRIBUTIONS
Kristina Veljkovic kristina@matf.bg.ac.rs

2010 Mathematics Subject Classification: 62E17, 62F10, 62G30, 62P30.
Key words: R control chart, Pearson distribution, positively skewed distribution, sample kurtosis, sample skewness.

In this paper, R control chart for positively skewed distributions is designed. For chosen exponential, gamma and Weibull distributions of quality characteristic, we calculated theoretical distribution of sample range and fitted corresponding Pearson distribution. Upper control limits and power of the R control chart were established, giving evidence of the goodness of fit of Pearson distributions to the theoretical distribution of sample range. For implementation of R control chart in practice, measures of sample skewness and kurtosis were compared and numerical example of construction of a proposed chart was given.