Canonical Forms for Families of Anti-commuting Diagonalizable Linear Operators

It is well known that a commuting family of diagonalizable linear operators on a finite dimensional vector space is simultaneously diagonalizable. In this paper, we consider a family A of anti-commuting (complex) linear operators on a finite dimensional vector space V. We prove that if the family is diagonalizable over the complex numbers, then V has an A-invariant direct sum decomposition into subspaces V_a such that the restriction of the family A to V_a is a representation of a Clifford algebra. Thus unlike the families of commuting diagonalizable operators, diagonalizable anti-commuting families cannot be simultaneously digonalized, but on each subspace, they can be put simultaneously to (non-unique) canonical forms. The construction of canonical forms for complex representations is straightforward, while for the real representations it follows from the results of [Bilge A.H., \c{S}. Ko\c{c}ak, S. U\u{g}uz, Canonical Bases for real representations of Clifford algebras, Linear Algebra and its Applications 419 (2006) 417-439. 3].Comment: This paper has been submitted to Linear Algebra and Its Application

The comparative study of nursing pads by electrospun cellulose acetate, polyethylene oxide and thermoplastic polyurethane nanofibers

This study summarizes the general information about nursing pads and novel electrospun nanofiber mats as potential component for nursing pads. It also compares electrospun thermoplastic polyurethane (TPU), cellulose acetate (CA) and polyethylene oxide (PEO) nanofibers with a polypropylene conventional disposable nursing pad (NP) in terms of hydrophilicity, breathability, air permeability and swelling properties. Nanofiber mats prepared by the electrospinning method have unique properties such as smooth surface, high specific surface area and high porosity with fine pores which will lead to improved wicking properties. These properties make nanofibers potential component for disposable nursing pads. Mean diameters of produced nanofibers were 284.39, 609.70 and 219.30 nm for CA, TPU and PEO, respectively. Water contact angle measurement revealed that these nanofibers show good wettability properties better than commercial nonwoven nursing mat and air permeability results revealed that these nanofibrous mats have considerably adequate permeability. Besides, water vapor permeability results showed these nanofibers still show good breathability despite their compact structure. © Published under licence by IOP Publishing Ltd

Nanofibers in face masks and respirators to provide better protection

A facemask is a loose-fitting, disposable device that creates a physical barrier between the mouth and nose of the wearer and potential contaminants in the immediate environment. They are generally labelled as surgical, isolation, dental or medical procedure masks. On the other hand, respirators are personal air purifiers. They are designed to protect the wearer from inhaling dangerous substances such as toxic chemicals and infectious particles. Respirators are designed to help reduce the wearer's respiratory exposure to airborne contaminants such as particles that are small enough to be inhaled - particles less than 100 microns (μm) in size. A face masks or a respirator consist entirely or substantially of filter material or comprises a face piece in which the main filter(s) form an inseparable part of the device. Nanofibers could be the key elements for filter materials in face masks or respirators. They have a very high surface area per unit mass that enhances capture efficiency and other surface area-dependent phenomena that may be engineered into the fiber surfaces (such as catalysis or ion exchange). They could enhance filter performance for capture of naturally occurring nanoparticles such as viruses, as well as micron-sized particles such as bacteria or man-made particles such as soot from diesel exhaust. © Published under licence by IOP Publishing Ltd

Canonical Forms For Families Of Anti-commuting Diagonalizable Linear Operators

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2010Bu çalışmada, sonlu boyutlu bir vektör uzayı üzerinde ters-değişmeli köşegenleştirilebilir lineer operatörler ailelerinin kanonik formlarını inceledik. Öncelikle, sonlu boyutlu bir vektör uzayında herhangi bir değişmeli köşegenleştirilebilir operatörler ailesinin eş zamanlı köşegenleştirilebilir olduğuna dair iyi bilinen bir sonucu verdik. Daha sonra sonlu boyutlu bir V vektör uzayı üzerinde ters-değişmeli köşegenleştirilebilir bir A operatörler ailesini ele aldık. Genel duruma bir yön çizmesi açısından iki ve üç elemanlı ters-değişmeli köşegenleştirilebilir lineer operatörler ailelerinin inşası için detaylı bir yapı verdik. Çalışmamızın ana sonucu, V’nin alt uzaylarına öyle bir A-invaryant direkt toplam dekompozisyonu vardır ki A’nın her alt uzaya kısıtlanışı ya sıfırdan farklı bir tane operatörden oluşur ya da bazı Clifford cebrilerinin bir temsilidir. Son olarak Clifford cebirlerinin reel ve kompleks temsillerinin sınıflandırılması ile ilgili bilgiler verdik.In this study, we examine canonical forms for families of anti-commuting diagonalizable linear operators on finite dimensional vector spaces. We begin with a well-known result on the simultaneous diagonalization of a family of commuting linear operators on a finite dimensional vector space which asserts that an arbitrary family of commuting diagonalizable operators can be simultaneously diagonalized. Then, we consider an anti-commuting family A of diagonalizable operators on a finite dimensional vector space V. In order to give a motivation for general case, we give a detailed construction for two and three element families of anti-commuting diagonalizable linear operators. Our main result is that V has an A-invariant direct sum decomposition into subspaces of V such that the restriction of the family to each summand either consists of a single nonzero operator or it is a representation of some Clifford algebra. Lastly, we give some classifications of real and complex representations of Clifford algebras.Yüksek LisansM.Sc

A Self-Tuning zSlices-Based General Type-2 Fuzzy PI Controller

The interval type-2 fuzzy Proportional-Integral (PI) controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance, which could be potentially due to the robust performance as a result of the smoother control surface around the steady state. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison with the type-1 fuzzy PI (T1-FPI) counterpart. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a tradeoff between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices-based general type-2 fuzzy PI controller (zT2-FPI), where the secondary membership functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an online manner. We will examine the effect of the SMF on the closed-system control performance to investigate their induced performance improvements. This paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies, where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared with the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems, in addition to real-world experiments that were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared with the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise, and uncertainties when compared with the type-1 and interval type-2 fuzzy counterparts

A big bang-big crunch optimization based approach for interval type-2 fuzzy PID controller design

In this paper, we will present a big bang-big crunch optimization (BB-BC) based approach for the design of an interval type-2 fuzzy PID controller. The implemented global optimization algorithm has a low computational cost and a high convergence speed. As a consequence, the BB-BC method is a very efficient search algorithm when the number of the optimization parameters is relatively big. The optimized type-2 fuzzy controller is compared with PID and type-1 fuzzy PID controllers which were optimized with either the BB-BC optimization method or conventional design strategies. The paper will also show the effect the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets on the closed loop system performance. We will present a comparative study performed on the highly nonlinear cascaded tank process to show the superiority of the optimized interval type-2 fuzzy PID controller compared to its optimized PID, type-1 counterparts. © 2013 IEEE

Evaluation of complications developing during and after transvaginal ultrasound — guided oocyte retrieval

Objectives: To investigate the complications of the oocyte retrieval procedure currently used in in vitro fertilisation. Material and methods: We examined 1.031 patients who underwent oocyte retrieval in the IVF unit of our hospital for complications developed during and after the procedure. Results: No complications developed related to sedation or general anaesthesia. Vaginal bleeding was observed in 3.1% of the patients. There was no intra-abdominal bleeding or pelvic organ injuries requiring surgery. Two patients developed pelvic abscesses. Ovarian hyperstimulation syndrome (OHSS) occurred in 1.45% of the patients. Almost all of the patients tolerated the oocyte retrieval process well. After the procedure, only 2% of the patients described their pain as severe, and 0.4% as the worst pain they had ever experienced. Conclusions: The most common complication during oocyte retrieval is vaginal bleeding, which is largely controlled by buffer application. In conclusion, the oocyte retrieval process can be considered a safe procedure

Electrospun Polyurethane Nanofibers

The electrospinning process is highlighted with the ability of fabricating fibers with diameters on the nanometer scale, small inter-fibrous pore size and high porosity, vast possibilities for functionalization with high surface area to volume or mass ratio, ease of use and instrument setup, and adaptability. It attracted a great deal of attention due to its unique properties. More than 100 different polymers have been successfully electrospun into ultrafine fibers using this technique including synthetic polymers such as polyurethane (PU). Electrospun PU nanofiber mats exhibiting good mechanical properties may have a wide variety of potential applications in high-performance air filters, protective textiles, wound dressing materials, sensors, drug delivery, etc. This chapter deals with the electrospinning of polyurethane nanofibers and their potential applications

Type-2 fuzzified flappy bird control system

In this study, we will present the novel application of Type-2 (T2) fuzzy control into the popular video game called flappy bird. To the best of our knowledge, our work is the first deployment of the T2 fuzzy control into the computer games research area. We will propose a novel T2 fuzzified flappy bird control system that transforms the obstacle avoidance problem of the game logic into the reference tracking control problem. The presented T2 fuzzy control structure is composed of two important blocks which are the reference generator and Single Input Interval T2 Fuzzy Logic Controller (SIT2-FLC). The reference generator is the mechanism which uses the bird's position and the pipes' positions to generate an appropriate reference signal to be tracked. Thus, a conventional fuzzy feedback control system can be defined. The generated reference signal is tracked via the presented SIT2-FLC that can be easily tuned while also provides a certain degree of robustness to system. We will investigate the performance of the proposed T2 fuzzified flappy bird control system by providing comparative simulation results and also experimental results performed in the game environment. It will be shown that the proposed T2 fuzzified flappy bird control system results with a satisfactory performance both in the framework of fuzzy control and computer games. We believe that this first attempt of the employment of T2-FLCs in games will be an important step for a wider deployment of T2-FLCs in the research area of computer games

Can evaluation of the cervix with histogram and Bishop scoring prior to birth induction forecast the birth type for superannuated primigravidas?

Purpose: We conducted this study to research both the forecasting efficiency of the cervical histogram and Bishop scoring for birth type (vaginal birth/cesarean) for the superannuated primigravida prior to birth induction. Methods: Ninety primigravidas in week 41 and beyond were included in the present study. Exclusions for the study included prior labor, ruptured membranes, any major uterine operations, cephalopelvic discord, fetal malpresentations, fetal anomalies, multiple pregnancy, placenta previa, vaginal bleeding, a high sensitivity for oxytocin usage, and an estimated fetal weight greater than 4000 g. Histogram hyperechogenic focus and hypoechogenic focus measurements are conducted in normal spontaneous birth (NSD) and cesarean (SECTIO) groups. Findings: Thirty-six patients had a cesarean birth, while 54 of the patients had vaginal births. On logarithmical regression analysis, the Bishop score and the parameters were found statistically significant in terms of proving the cesarean indication (p=0.001). In our cervical histogram, the forecasting efficiency of the hyperechogenic focus and hypoechogenic focus measurements for determining the birth type were not been able to shown (p=0.089 ; p=0.555). Bishop scoring parameters showed statistically significant deviances between the NSD group compared to the cesarean group in terms of a 1-2 cm increase in cervical opening and for being 3-4 cm(p=0.0001), the cervical extinguishment as 40%-50% (p=0.0001), the occurrence of cervical softening (p=0.0001), and the head level at -1 and -2 (p=0.0001). When declaring the cesarean indication, the Bishop score’s AUC value was found as 0.932 and the LR(+) value as 9; while the estimation value for the Bishop score occurring below \u3c5 increased the cesarean birth risk ninefold. Conclusion: During a superannuated nulliparous pregnancy, the Bishop score and the Bishop score’s individual parameters are meaningful for vaginal birth, while a cervical histogram is not significant for forecasting the birth type