New travelling wave solutions to the Ostrovsky equation

In this work, new travelling wave solutions to the Ostrovsky equation are studied by employing the improved tanh function method. With this method, the Ostrovsky equation is reduced to the nonlinear ordinary differential equation and then the different types of exact solutions are derived based on the solutions of the Riccati equation. We will compare our solutions with those gained by the other methods.     

Radionuclides in steel slag intended for road construction

The objective of this study was to describe the radiochemical characteristics of electric arc furnace (EAF) slag from Croatian EAF black steel slags, generated from carbon steel production process in CMC Sisak d.o.o., and steel mill in Split in order to enhance the understanding of possibilities for their use in road construction. This article presents the results of radionuclide in electric arc furnace steel slag. The presence of natural isotopes ⁴⁰K, ²³²Th (²²⁸Ra), ²²⁶Ra and ²³⁸U was established. The measured activity in slag natural isotopes lies within the Croatian legally permitted limits.     

Alkaline Earth–Olefin Complexes with Secondary Interactions

Strontium and calcium (alkaline earth: Ae) olefin complexes stabilised by secondary Ae???F?C and β‐agostic Ae???H?Si interactions are presented. Olefin coordination onto the alkaline earths is plain in the solid state, and it is thermodynamically favoured over the coordination of THF. The existence of the Ae???olefin interactions is corroborated by solution NMR data and DFT computations. The coordination mode of the olefin varies with steric effects and, if enforced, olefin dissociation can be compensated by the other non‐covalent interactions, as supported by DFT computations.     

Some relations between certain inequalities concerning analytic and univalent functions

By making use of the well-known assertions in [S.S. Miller, P.T. Mocanu, Differential Subordinations, Theory and Applications, Marcel Dekker, New York-Basel, 2000] and [M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A Math. Sci. 69 (7) (1993) 234–237], several useful results of certain inequalities dealing with analytic and univalent functions are obtained and then certain consequences of them are also indicated.     

On some generalized sequence spaces of fuzzy numbers defined by a sequence of Orlicz functions

The purpose of the paper is to introduce the concepts of almost λ-statistical convergence and strongly almost λ-convergence of sequences of fuzzy numbers. We establish some connections between these concepts. It is also shown that if a sequence of fuzzy numbers is strongly almost λ-convergent with respect to a sequence of Orlicz funtions then it is almost λ-statistical convergent.     

Irreducibility, Brill-Noether loci, and Vojta's inequality

This paper deals with generalizations of Hilbert's irreducibility theorem. The classical Hilbert irreducibility theorem states that for any cover of the projective line defined over a number field , there exist infinitely many -rational points on the projective line such that the fiber of over is irreducible over . In this paper, we consider similar statements about algebraic points of higher degree on curves of any genus. We prove that Hilbert's irreducibility theorem admits a natural generalization to rational points on an elliptic curve and thus, via a theorem of Abramovich and Harris, to points of degree 3 or less on any curve. We also present examples that show that this generalization does not hold for points of degree 4 or more. These examples come from an earlier geometric construction of Debarre and Fahlaoui; some additional necessary facts about this construction can be found in the appendix provided by Debarre. We exhibit a connection between these irreducibility questions and the sharpness of Vojta's inequality for algebraic points on curves. In particular, we show that Vojta's inequality is not sharp for the algebraic points arising in our examples.

     

New Coherent States for the BDS-Hamiltonian

In the paper we construct a new set of coherent states for a deformed Hamiltonian of the harmonic oscillator, previously introduced by Beckers, Debergh, and Szafraniec, which we have called the BDS-Hamiltonian. This Hamiltonian depends on the new creation operator a ⁺, i.e. the usual creation operator displaced with the real quantity . In order to construct the coherent states, we use a new measure in the Hilbert space of the Hamiltonian eigenstates, in fact we change the inner product. This ansatz assures that the set of eigenstates be orthonormalized and complete. In the new inner product space the BDS-Hamiltonian is self-adjoint. Using these coherent states, we construct the corresponding density operator and we find the P-distribution function of the unnormalized density operator of the BDS-Hamiltonian. Also, we calculate some thermal averages related to the BDS-oscillators system which obey the quantum canonical distribution conditions.     

Charge and spin structure in of YBa(2)Cu(3)O(6.35)

Neutron scattering has been used to measure the charge and spin structure in the highly underdoped superconductor YBa(2)Cu(3)O(6.35). Incommensurate static charge ordering is found that remains at high temperatures. The magnetic pattern is complex with a resonance and incommensurate structure observed at low temperatures. The results clarify the role of striped phases in YBa(2)Cu(3)O(6+x) superconductors.