Mathematics

In the present paper, we introduce the concept of Δ m − statistical boundedness of real (or complex) numbers sequences by using generalized difference operator Δ m and examine relationships between Δ m − statistical convergence, Δ m − statistical Cauchiness and Δ m − statistical boundedness. In addition to that we compute the Köthe-Toeplitz and generalized Köthe-Toeplitz duals of the set of all Δ m − statistical bounded sequences. Moreover, we come up with the idea of statistical α and β duals of the sets of sequence which makes us capable of creating statistical equivalents of the notions of normality and perfectness of sequence spaces.

In this paper, we introduce the concepts of ?m-deferred statistical convergence of order ? and strong ?mr-deferred Ces?ro summability of order ? of real sequences. Additionally, some inclusion relations about ?m-deferred statistical convergence of order ? and strong ?mr-deferred Ces?ro summability of order ? are given.

The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence for nets in Riesz spaces by using the finite additive measures on directed sets. Moreover, we give some relations among the statistical convergence and the lattice properties such as the order convergence and lattice operators.

In this paper, we compute H-norm of a transfer matrix, via bisection algorithm. The algorithm is given and applied some problems. The problems are choosen from various areas of control theory such as aircraft models and decentralized interconnected systems.

Background: Freshwater snails are the intermediate hosts of a large variety of trematode flukes such as Schistosoma mansoni responsible for one of the most important parasitic diseases caused by helminths, affecting 67 million people worldwide. Recently, the WHO Global Vector Control Response 2017-2030 (GVCR) programme reinforced its message for safer molluscicides as part of required strategies to strengthen vector control worldwide. Here, we present the essential oil from Eryngium triquetrum as a powerful product with molluscicide and parasiticide effect against S. mansoni and the snail intermediate host Biomphalaria glabrata. Methods: In the present study, we describe using several experimental approaches, the chemical composition of E. triquetrum essential oil extract and its biological effects against the snail B. glabrata and its parasite S. mansoni. Vector and the free-swimming larval stages of the parasite were exposed to different oil concentrations to determine the lethal concentration required to produce a mortality of 50% (LC 50) and 90% (LC 90). In addition, toxic activity of this essential oil was analyzed against embryos of B. glabrata snails by monitoring egg hatching and snail development. Also, short-time exposure to sublethal molluscicide concentrations on S. mansoni miracidia was performed to test a potential effect on parasite infectivity on snails. Mortality of miracidia and cercariae of S. mansoni is complete for 5, 1 and 0.5 ppm of oil extract after 1 and 4 h exposure. Results: The major chemical component found in E. triquetrum oil determined by GC-FID and GC/MS analyses is an aliphatic polyacetylene molecule, the falcarinol with 86.9-93.1% of the total composition. The LC 50 and LC 90 values for uninfected snails were 0.61 and 1.02 ppm respectively for 24 h exposure. At 0.5 ppm, the essential oil was two times more toxic to parasitized snails with a mortality rate of 88.8 ± 4.8%. Moderate embryonic lethal effects were observed

In this paper, conformable fractional order differential equations with piecewise constant arguments are used for a modeling population density of a bacteria species in a microcosm. The discretization process of a differential equation with piecewise constant arguments gives us two dimensional discrete dynamical system in the interval t ∈ [nh, (n + 1)h). By using the center manifold theorem and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip and Neimark-Sacker bifurcation depending on the parameter r. It is observed that the model describes some biological phenomena for a bacteria population such as homogeneous bacteria distributions and inhomogeneous spatial population distributions. In addition, the effect of fractional order derivative on dynamic behavior of the system is investigated. Finally, all theoretical results are supported by numerical simulations.