The random walk on the random connection model

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$, where $d$ denotes the dimension of the underlying Euclidean space. More precisely, focus is on the random connection model in which the vertex set is given by the realization of a homogeneous Poisson point process. We show that this random graph exhibits the same properties as classical discrete long-range percolation models studied in [3] with regard to recurrence and transience of the random walk. The recurrence results are valid for every intensity of the Poisson point process while the transience results hold for large enough intensity. Moreover, we address a question which is related to a conjecture in [16] for this graph.Comment: New version of the manuscript with some extension

Max-linear models on infinte graphs generated by Bernoulli bond percolation

We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph $\mathbb{Z}^2$ and nearest neighbor bond percolation. Focus is on the dependence introduced by this graph into the max-linear model. As a natural application we consider communication networks, in particular, the distribution of extreme opinions in social networks.Comment: 18 page

Graph distances of continuum long-range percolation

We consider a version of continuum long-range percolation on finite boxes of $\mathbb{R}^d$ in which the vertex set is given by the points of a Poisson point process and each pair of two vertices at distance $r$ is connected with probability proportional to $r^{-s}$ for a certain constant $s$. We explore the graph-theoretical distance in this model. The aim of this paper is to show that this random graph model undergoes phase transitions at values $s=d$ and $s=2d$ in analogy to classical long-range percolation on $\mathbb{Z}^d$, by using techniques which are based on an analysis of the underlying Poisson point process

On the distances within cliques in a soft random geometric graph

We study the distances of edges within cliques in a soft random geometric graph on a torus, where the vertices are points of a homogeneous Poisson point process, and far-away points are less likely to be connected than nearby points. We obtain the scaling of the maximal distance between any two points within a clique of size $k$. Moreover, we show that asymptotically in all cliques with large distances, there is only one remote point and all other points are nearby. Furthermore, we prove that a re-scaled version of the maximal $k$-clique distance converges in distribution to a Fr\'echet distribution. Thereby, we describe the order of magnitude according to which the largest distance between two points in a clique decreases with the clique size

On the existence and regularity of local times

We study the existence and regularity of local times for general $d$-dimensional stochastic processes. We give a general condition for their existence and regularity properties. To emphasize the contribution of our results, we show that they include various prominent examples, among others solutions to stochastic differential equations driven by fractional Brownian motion, where the behavior of the local time was not fully understood up to now and remained as an open problem in the stochastic analysis literature. In particular this completes the picture regarding the local time behavior of such equations, above all includes high dimensions and both large and small Hurst parameters. As other main examples, we also show that by using our general approach, one can quite easily cover and extend some recently obtained results on the local times of the Rosenblatt process and Gaussian quasi-helices

Leaching of scrap lead acid battery paste by NaOH

Zehirli malzeme olarak sınıflandırılan kurşunu içeren birçok ürün, son yıllarda, kullanım alanını kaybetmektedir. Kurşunun en yaygın kullanım alanını kurşun asit akümülatörleri oluşturmaktadır. Kurşun asit akümülatörlerinin kullanım ve tüketim miktarları, çevreye karşı etkileriyle birlikte göz önüne alındığında, geri kazanımının gerekliliğini ve önemini yansıtmaktadır. Nitekim son yıllarda, Avrupa’da, %95’in üzerinde hurda kurşun asit akümülatörü geri kazanılmaktadır. Geri kazanımda temel aşamalar, sırasıyla; akümülatör asidinin boşaltılması, plastik kısımların ayrılması, metalik kısımların değerlendirilmesi ve akümülatör pastasının geri kazanılması süreçleridir. Hurda kurşun asit akümülatörlerinin geri kazanımında hidrometalurjik ve pirometalurjik yöntemler uygulanmaktadır. Bu yöntemler içerisinde, doğrudan ergitmeye dayanan yöntemlerin, gerek düşük metal kazanma verimi gerekse çevre açısından olumsuz etkileri nedeniyle yeni yöntemlerin geliştirilmesi gerekmektedir. Geri kazanım sürecinde, karmaşık kimyasal yapılı atık akümülatör pastasında bulunan, özellikle, zor çözünen PbO2 ve kükürt içerikli PbSO4 büyük sorun yaratmaktadır. Bu çalışmada, atık kurşun asit akümülatörlerinde bulunan akümülatör pastasının kimyasal ve fiziksel karakterizasyonu yapılmakta, ardından NaOH çözeltileriyle çözümlendirilmesi şartları incelenmektedir. NaOH ile çözümlendirmede en uygun işlem şartları; 400 dev.dak–1 karıştırma hızında, 1/10 katı/sıvı oranı için 0.7 M NaOH başlangıç çözeltisiyle, 15 dakikalık çözümlendirme süresinde ve ortam sıcaklığında sağlanmaktadır. X-ışını difraksiyonu analizi sonuçlarına göre, işlem sonrasında akümülatör pastasındaki PbSO4, kurşun oksi-hidroksit (Pb3O2(OH)2) bileşiğine dönüşmektedir. İşlem sonrasında atık pastada %68.8 oranında bulunan PbSO4, çözümlendirme sonrasında  %0.5 oranında analiz edilmektedir. Anahtar Kelimeler: Geri kazanım, akümülatör pastası, kurşun akümülatörler, NaOH çözümlendirmesi.Many lead based products that are classified as toxic material have disappeared from use in recent years. Lead acid batteries constitute the most widespread usage area of lead. Lead is particularly suitable for batteries, because of its characteristics (conductivity, resistance to corrosion and the special reversible reaction between lead oxide and sulphuric acid). The majority of lead / acid batteries are used as SLI batteries (starting, lightning and ignition) for the purpose of starting the engines of cars and lorries. Another sort of lead acid battery is the traction battery, used to power electric vehicles such as milk floats, forklift trucks and airport support vehicles. This type of battery provides the best service for "stop and start" conditions. A last sort of lead acid battery concerns stationary battery, which provides uninterrupted electrical power (e.g. in hospitals, telephone exchanges, companies etc.) The active mass, cathode, anode, connecting bridges, electrolyte, and casing are the main components of lead acid battery. The cathode (positive pole) consists of metallic lead, whereas anode (negative pole) consists of lead oxides. Connecting bridges are made of suitable lead-antimony, lead-calcium (tin, aluminium) alloys with additives in negligible quantities, such as copper, arsenic, tin and selenium. Sulphuric acid solution is used as an electrolyte in which lead-antimony plates are immersed. Casing is usually made of polypropylene, and, less frequently, of hard rubber, ebonite, bakelite etc. Other components of lead acid batteries are paper, rubber, fibre-glass and wood. When a battery discharges, as it operates the starting motor of a car, the concentration of sulphuric acid decreases from the electrolyte and the lead from the electrodes is transformed into lead sulphate. As the concentration of the acid decreases, the density of the electrolyte also decreases, thus making it possible to know the level of charge of a battery by measuring the density of its solution. For each electron generated in an oxidation reaction occurring at the negative electrode, there is an electron consumed in the reaction of the reduction of the positive electrode. As the process continues, the active materials (the lead oxides paste and the porous lead) are depleted and the speed of the reaction decreases until the battery is no longer able to supply electrons. Most of the lead oxides paste and the porous lead are converted into lead sulphate. When a battery is recharged, these reactions are inverted and the lead sulphate changes back into lead and lead oxide. In time, the lead oxide plates become contaminated by lead sulphate form sludge layer (55-60% PbSO4; 20-25% PbO; 1-5% PbO2; 1-5% metallic Pb). This mixture accumulates at the bottom of the battery. It is no longer possible for battery to recharge due to the high level of contamination. From this moment the battery becomes what is known to be a spent battery. The usage amount and the consumption of lead acid batteries, considering the environmentally non-friendly effects, reflect the necessity and the importance of recycling. Likewise, in recent years more than 95% of scrap lead acid batteries have been recycled in Europe. Basic stages in lead acid battery recycling processes are removal of the battery acid, separation of the plastic parts, processing of metallic parts, recycling of battery paste, respectively. Hydrometallurgical and pyrometallurgical methods are used in scrap lead acid battery recycling. During recycling process, particularly, because of non-soluble PbO2 and sulphur containing PbSO4, significant problems occur. The presence of lead sulphate complicates the environmentally acceptable treatment of the battery paste. The high temperatures required to decompose the sulphate generate lead fumes in addition to dilute SO2 gas streams. PbO2 can only be dissolved by using additional chemicals in hidro-electrometallurgical recycling processes. In this study, lead acid batteries were defined, and some existing pyrometallurgical and hydro-electrometallurgical scrap lead acid battery treatment processes were comparatively investigated. The purpose of this study is to investigate the possibility for desulphurization of the paste with sodium hydroxide to verify the possibility for removal of sulphur ions in the form of sodium sulphate. Optimum process conditions for NaOH leaching of battery paste are achieved as follows; 400 rpm of stirring rate, 1/10 of solid/liquid ratio for 0.7 M NaOH starting solution, 15 minutes of leaching duration at room temperature. X-ray diffraction analysis show the transformation of PbSO4 in the battery paste into lead oxi-hydroxide (Pb3O2(OH)2) compound.Keywords: Recycling, battery paste, lead batteries, NaOH leaching

Electrophysiological Correlation and Gradation of Patients Prediagnosed With Carpal Tunnel Syndrome

DergiPark: 378999tmsjAims: In this study, it is aimed to detect electrophysiological correlation of patients who were referred to TrakyaUniversity Medical Research Center Neurology Clinics Electromyography (EMG) lab in 2014 with Carpal Tunnel Syndrome (CTS) pre-diagnosis and grade them based on electrophysiological features.Methods: Electromyography (EMG) records of 174 patients who were sent to electromyography lab in 2014 withCarpal Tunnel Syndrome (CTS) pre diagnosis were scanned retrospectively. Patients were recorded with the data of gender and age. Correlation between pre diagnosis and electrophysiological diagnosis were reported statistically by using Kappa and McNemar tests. Patients were classified based on sex using Chi-square test. Number and percentages, arithmetic mean± standard deviation, median (minimum-maximum) were used as descriptive analysis. Results: Out of all electrophysiological diagnosis, 62 patients (35.6%) were consistent with pre diagnosis when 112(64.4%) were inconsistent. Out of patients who were diagnosed with Carpal Tunnel Syndrome (CTS) according to their electromyography (EMG) findings, 31 patients (48.4%) had mild syndrome.Conclusion: A big inconsistency between pre diagnosis and electromyography (EMG) results was detected. It isimportant to make a more careful and detailed examination to fix this proble