Some Decision Problems for Extended Modular Groups

In this paper we investigate solvability of the word problem for Extended Modular groups, Extended Hecke groups and Picard groups in terms of complete rewriting systems. At the final part of the paper we examine the other important decision problem (conjugacy problem) for only Extended Modular groups

Detecting bifurcations in dynamical systems with CROCKER plots

Existing tools for bifurcation detection from signals of dynamical systems typically are either limited to a special class of systems, or they require carefully chosen input parameters, and significant expertise to interpret the results. Therefore, we describe an alternative method based on persistent homology -- a tool from Topological Data Analysis (TDA) -- that utilizes Betti numbers and CROCKER plots. Betti numbers are topological invariants of topological spaces, while the CROCKER plot is a coarsened but easy to visualize data representation of a one-parameter varying family of persistence barcodes. The specific bifurcations we investigate are transitions from periodic to chaotic behavior or vice versa in a one-parameter family of differential equations. We validate our methods using numerical experiments on ten dynamical systems and contrast the results with existing tools that use the maximum Lyapunov exponent. We further prove the relationship between the Wasserstein distance to the empty diagram and the norm of the Betti vector, which shows that an even more simplified version of the information has the potential to provide insight into the bifurcation parameter. The results show that our approach reveals more information about the shape of the periodic attractor than standard tools, and it has more favorable computational time in comparison to the Rosenstein algorithm for computing the Lyapunov exponent from time series

Conjugacy for Free Groups under Split Extensions

At the present paper we show that conjugacy is preserved and reflected by the natural homomorphism defined from a semigroup S to a group G, where G defines split extensions of some free groups. The main idea in the proofs is based on a geometrical structure as applied in the paper [8]

Comparison of the calculated absorption and the measured field strength of HF waves reflected from the ionosphere

The absorption (L) of the wave in the ionosphere has been calculated. The 5.47MHz wave is transmitted from Ercis, Turkey (39.03°N, 43.37°E)and received at Elazıg, Turkey (38.70°N, 39.20°E). The field strength of this wave is measured by ITU-Compliant HF Field Strength Monitoring Terminal, and the absorption L in the ionosphere has been calculated. It is observed that the field strength of the wave is least around noon time and it increases at night times at all seasons. The diurnal and seasonal variations of the calculated absorption L shows that the maximum absorption in the wave occurs around noon time. The behaviour of the diurnal and seasonal variations of the field strength of the wave can be explained with the diurnal and seasonal variations of the calculated absorption L in the ionosphere. Equation (22) in this paper can be used to obtain the imaginary part (β) of the refractive index of the ionospheric plasma, and it can be applied to the HF radio waves propagations in the ionosphere for absorption L

The next step of the word problem over monoids

It is known that a group presentation P can be regarded as a 2-complex with a single 0-cell. Thus we can consider a 3-complex with a single 0-cell which is known as a 3-presentation. Similarly, we can also consider 3-presentations for monoids. In this paper, by using spher- ical monoid pictures, we show that there exists a finite 3-monoid-presentation which has unsolvable ‘‘generalized identity problem’’ that can be thought as the next step (or one- dimension higher) of the word problem for monoids. We note that the method used in this paper has chemical and physical applications

Red Cell Distribution Width and Acute Complications of Diabetes

Context. Red cell distribution width (RDW) has been associated with type 2 diabetes (T2DM), however data in relation to diabetic ketoacidosis (DKA) and hyperglycemic hyperosmolar non-ketotic acidosis (HONK) remains unclear. Objective. The aim of this study was to evaluate the association between RDW, MCV, and RDW/MVC values and acute complications in T2DM. Patients and Methods. RDW was measured in 90 T2DM patients (30 DKA, 30 HONK and 30 T2DM without acute complications). Clinical variables were analyzed by One -Way ANOVA, Kruskal-Wallis and Pearson analysis with SPSS software. Diagnostic screening tests and ROC curve analysis determined the cut-off point of MCV,RDW and RDW/MCV values. Results. DKA patients had higher levels of plasma glucose (524.20 +/- 201.43mg/dL, p<0.001), HbA1c (10.73 +/- 2.29%, p<0.001), osmotic pressure (310.32 mosm/L, p<0.001), RDW (14.61 +/- 1.75g/L, p<0.01), and the RDW/MCV ratio (0.17 +/- 0.04%, p<0.01), compared to HONK patients. RDW/MCV cut-off value was 0.15 with 90% sensitivity 50% specifity these values for only MCV were 76.67%-70%, for only RDW were 76.67%-63.33% respectively. The area under curve values for the ability to reflect DKA for RDW and the RDW/MCV ratio were 0.708 and 0.766, respectively (p<0.001). Conclusions. RDW and RDW/MCV ratio were found associated with DKA and valuable in predicting DKA. However these parameters were not valuable in predicting HONK

Finite derivation type for graph products of monoids

Bu çalışma, 08-11, Ağustos 2014 tarihlerinde Gyeongju[Güney Kore]’de düzenlenen 22. International Conference on Finite and Infinite Dimensional Complex Analysis and Applications (ICFIDCAA) Kongresi‘nde bildiri olarak sunulmuştur.The aim of this paper is to show that the class of monoids of finite derivation type is closed under graph products.Balıkesir Üniversitesi - 2014/95, 2015/4

Biologically modified microelectrode sensors provide enhanced sensitivity for detection of nucleic acid sequences from Mycobacterium tuberculosis

This paper describes improved sensitivity when using biosensors based on microfabricated microelectrodes to detect DNA, with the goal of progressing towards a low cost and mass manufacturable assay for antibiotic resistance in tuberculosis (TB). The microelectrodes gave a near 20 times improvement in sensitivity compared to polycrystalline macroelectrodes. In addition, experimental parameters such as redox mediator concentration and experimental technique were investigated and optimised. It was found that lower concentrations of redox mediator gave higher signal changes when measuring hybridisation events and, at these lower concentrations, square wave voltammetry was more sensitive and consistent than differential pulse voltammetry. Together, this paper presents a quantifiable comparison of macroelectrode and microelectrode DNA biosensors. The final assay demonstrates enhanced sensitivity through reduction of sensor size, reduction of redox mediator concentration and judicious choice of detection technique, therefore maintaining manufacturability for incorporation into point of care tests and lab-on-a-chip devices