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Magnetic curves represent trajectories of charged particles moving on a Riemannian manifold under the action of a magnetic field. The study of magnetic curves in arbitrary Riemannian manifolds was developed in early 1990's, even though related works can be found earlier. Recently there are interesting results on magnetic curves in Euclidean space, Sasakian manifolds, cosymplectic manifolds, Sol space and quasi Sasakian manifolds. In this talk we consider magnetic curves with respect to the almost cosymplectic structure of the Sol space.

We consider the discrete Jensen-Mercer inequality and Chebyshev's inequality of the Mercer type. We present bounds for Chebyshev's functional of the Mercer type and bounds for the Jensen-Mercer functional in terms of the discrete Ostrowski inequality. We show how these results can be used to establish new refinements of the considered inequalities.

I will survey a number of recent results concerned with both topological and smooth linearization of several classes of nonautonomous dynamical systems. The talk will be based on joint works with Lucas Backes, Ken Palmer, Weinian Zhang and Wenmeng Zhang.

In this paper we obtain few valuable identities by using Lidstone's polynomial. Further, the identities were applied for constructing new generalizations of Steffensen's inequality, namely for (2n)-convex and (2n + 1)-convex functions. In addition, using Cebysev and Gruss type inequalities we consider the bounds for the integrals in the perturben versions of the previously described identities. Moreover, elated Ostrowski type inequalities are given.

In this work, we present the modification of the existing algorithm for the search of the extremal Z4-codes and new extremal Z4-codes, of lengths 32 and 40, obtained by its application.

In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results generalized known inequalities involving the Hardy operator. We also get new inequalities involving the classical Hardy–Hilbert inequality.

One of the most common technique to study a nonlinear dynamics is to find an equivalent linear dynamics. The process of constructing a map, which transforms a nonlinear dynamics into a linear dynamics is commonly known as Linearization. Let ( X , ∥ ⋅ ∥ ) be an arbitrary Banach space and let B := {; ϕ : Z − → X ∣ ∣ ∥ ϕ ∥ B < ∞ }; be a Banach space of sequences with appropriate norm ∥ ⋅ ∥ B . Given m ∈ Z + and a sequence x : Z → X , define a new sequence x m : Z − → X given by x m ( j ) := x ( m + j ) for all j ∈ Z − . In this talk, I am going to present a result on the Linearization of Difference equation with infinite delay, x ( m + 1 ) = A m x m + f m ( x m ) for all m ∈ Z + , (1) in a Banach Space X . Here we assume that for each m ∈ Z + , A m : B → X is a bounded linear map and the perturbation ( f m ) m ∈ Z + is small and Lipschitz. In this result, a sequence of continuous and one-one maps, ( h m ) m ∈ Z + , is constructed which gives equivalency between the nonlinear dynamics (1) and its linear counterpart. We also showed that when ( A m ) m ∈ Z + admits exponential dichotomy, our result is applicable.

We present the Chebyshev-Steffensen inequality involving the inner product on the real m-space, and some new upper bounds for the weighted Chebyshev-Steffensen functional as well as the Jensen-Steffensen functional involving the inner product under various conditions. We show how these results can be used to establish new upper bounds for the Jensen-Steffensen functional for certain generalized convex functions such as P- convex functions and functions with nondecreasing increments.

In this talk, we will give bounds for identities related to generalizations of Steffensen's inequality by using weighted Hermite-Hadamard inequalities. As we will show these bounds can be obtained by utilizing Holder's inequality and convex or concave functions of the form $|f^{; ; (n)}; ; |^q$, for $n\geq 2$ and $q\geq 1$.

Motivated by some recent investigations about the sharpness of the Jensen inequality, this poster presentation deals with the sharpness of the converse of the Jensen inequality. These results are then used for deriving new inequalities for different types of generalized f-divergences. As divergences measure the differences between probability distributions, these new inequalities can also be applied on the Zipf-Mandelbrot law as a special kind of a probability distribution.

For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The limiting process consists of an $\alpha$--stable L\'{e}vy process and an extremal process. We also describe the dependence between these two components of the limit. The convergence takes place in the space of $\mathbb{R}^{2}$--valued c\`{a}dl\`{a}g functions on $[0,1]$, with the Skorohod weak $M_{1}$ topology. We further show that this topology in general can not be replaced by the stronger (standard) $M_{1}$ topology., Comment: arXiv admin note: text overlap with arXiv:1607.03788