In this paper, a relationship between the zeros and critical points of a polynomial p(z) is established. The relationship is used to prove Sendov's conjecture in some special cases.

In this thesis we employ computer simulations and statistical physics to understand the origin of liquid-liquid phase transitions and their relationship with anomalies typical of liquid water. Compared with other liquids, water has many anomalies. For example the density anomaly: when water is cooled below 4 C the density decreases rather than increases. This and other anomalies have also been found to occur in a few other one-component liquids, sometimes in conjunction with the existence of a liquid-liquid phase transition (LLPT) between a low-density liquid (LDL) and a high-density liquid (HDL). Using simple models we explain how these anomalies arise from the presence of two competing length scales. As a specific example we investigate the cut ramp potential, where we show the importance of "competition" in this context, and how one length scale can sometimes be zero. When there is a clear energetic preference for either LDL or HDL for all pressures and temperatures, then there is insufficient competition between the two liquid structures and no anomalies occur. From the simple models it also follows that anomalies can occur without the presence of a LLPT and vice versa. It remains therefore unclear if water has a LLPT that ends in a liquid-liquid critical point (LLCP), a hypothesis that was first proposed based on simulations of the ST2 water model. We confirm the existence of a LLCP in this model using finite size scaling and the Challa-Landau-Binder parameter, and show that the LLPT is not a liquid-crystal transition, as has recently been suggested. Previous research has indicated the possible existence of a LLCP in liquid silica. We perform a detailed analysis of two different silica models (WAC and BKS) at temperatures much lower than was previously simulated. Within the accessible temperature range we find no LLCP in either model, although in the case of WAC potential it is closely approached. We compare our results with those obtained for other tetrahedral liquids and conclude that insufficient "stiffness" in the Si-O-Si bond angle might be responsible for the absence of a LLCP.

The aim of thesis is a system of critical points in food production, especially in the production of confectionery products. The system is based on the ability of manufacturers to establish the critical aspects of the production of safe food, allows to systematically identify hazards and assess the probability of its occurrence during production. Danger primarily as a substance in food, which could result in adverse health effects for consumers. And subsequently helps to improve the effectiveness of controls. This concept of control techniques is apparented from the national and European legislative requirements, which are listed in the first theoretical part of this thesis. They are designed to better acquaint themselves with the general requirements that are placed on food manufacturers. With the entry into the European Union is integrated European legislation, national legislation incorporated in European policy and legal requirements are taken into national legislation the second part introduces the principles and procedures of the system of critical points. Many manufacturing processes involve multi-process from producing raw materials for the finished product. Correct, complete, and introduced the study of critical points identified by the system and regulate the factors that directly affect the safety of products. Identification and monitoring of critical points is more cost effective than the method of quality assurance inspection and testing of finished product. Records and documentation are the perfect evidence that all measures have been taken and were given the duty of care to prevent problems. In the final section is a common procedure for a system of critical points compared with an established system for a particular product. The specific products will be demonstrated readiness and capacity of the undertaking to establish a system for all products or product groups, which will subsequently be evaluated. The purpose of thesis is carefully and thoroughly analyze the system by the critical points in the manufacture of confectionery, but prove that we are able to prepare for the strict legal conditions and the hard and fierce competition. This development does not stop or avoid it, have no other than to respond promptly to these developments and to adapt in order to produce the desired changes brought about by the success and to our food industry was at a level as we wish, but also as your own work and creativity deserve. Not in vain proverb holds that "Happiness wishes prepared.

GaAs(1-x)Bi(x) (x = 0 to 17%) optical properties were investigated by spectroscopic ellipsometry (in energy ranges of 0.37–9.0 eV). Optical features in the dielectric function, known as the critical points, were distinguished and modeled using standard analytic line shapes. The energy dependence of the critical points energies was thoroughly investigated as a function of Bi content and thin film strain. Critical points analysis in the Brillion zone showed that the top of the valence band is most strongly dependent on Bi content compared to other parts of the band structure. In addition, an interesting new critical point was observed that is attributed to alternative allowed optical transitions made possible by changes to the top of the valence band caused by resonant interactions with Bi orbitals. Several of the critical points were extrapolated to 100% Bi and showed reasonable agreement with the calculated band structure of GaBi. GaAs(1-x)Bi(x) (x= 03, 0.7 and 1.1%) based p+/n and n+/p heterostructure photovoltaic performance was characterized through IV and CV measurement. By introduction of Bi into GaAs, a non-zero EQE below the GaAs band edge energy was observed while the highest efficiency was obtained by ~ 0.7% Bi incorporation. EQE spectrum was modeled to find the minority carrier diffusion lengths of ~ Ln = 1600 and Lp = 140 nm for p-doped and n-doped GaAs92Bi08 in the doping profile of 10^15 - 10^16 cm^-3. Analysis of the CV measurement confirmed the background n-doping effect of Bi atom and the essential role of the cap layer to reduce multi-level recombination mechanisms at the cell edge to improve ideality factor. Low temperature grown GaAs was optimized to be used as photoconductive antenna in THz time-domain spectroscopy setup. The As content was investigated to optimize photo-carrier generation using 1550 nm laser excitation while maintaining high mobility and resistivity required for optical switching. A barrier layer of AlAs was added below the LT-GaAs to limit carrier diffusion into the GaAs substrate. Moreover, LT-GaAs layer thickness and post-growth annealing condition was optimized. The optimized structure (2-µm LT-GaAs on 60-nm AlAs, under As2:Ga BEP of ~7, annealed at 550°C for 1 minute) outperformed a commercial InGaAs antenna by a factor of 15 with 4.5 THz bandwidth and 75 dB signal-to-noise ratio at 1550 nm wavelength. / Graduate

This dissertation was to study computational theory and methods for ?nding multiple saddle critical points in Banach spaces. Two local minimax methods were developed for this purpose. One was for unconstrained cases and the other was for constrained cases. First, two local minmax characterization of saddle critical points in Banach spaces were established. Based on these two local minmax characterizations, two local minimax algorithms were designed. Their ?ow charts were presented. Then convergence analysis of the algorithms were carried out. Under certain assumptions, a subsequence convergence and a point-to-set convergence were obtained. Furthermore, a relation between the convergence rates of the functional value sequence and corresponding gradient sequence was derived. Techniques to implement the algorithms were discussed. In numerical experiments, those techniques have been successfully implemented to solve for multiple solutions of several quasilinear elliptic boundary value problems and multiple eigenpairs of the well known nonlinear p-Laplacian operator. Numerical solutions were presented by their pro?les for visualization. Several interesting phenomena of the solutions of quasilinear elliptic boundary value problems and the eigenpairs of the p-Laplacian operator have been observed and are open for further investigation. As a generalization of the above results, nonsmooth critical points were considered for locally Lipschitz continuous functionals. A local minmax characterization of nonsmooth saddle critical points was also established. To establish its version in Banach spaces, a new notion, pseudo-generalized-gradient has to be introduced. Based on the characterization, a local minimax algorithm for ?nding multiple nonsmooth saddle critical points was proposed for further study.

This dissertation was to study computational theory and methods for ?nding multiple saddle critical points in Banach spaces. Two local minimax methods were developed for this purpose. One was for unconstrained cases and the other was for constrained cases. First, two local minmax characterization of saddle critical points in Banach spaces were established. Based on these two local minmax characterizations, two local minimax algorithms were designed. Their ?ow charts were presented. Then convergence analysis of the algorithms were carried out. Under certain assumptions, a subsequence convergence and a point-to-set convergence were obtained. Furthermore, a relation between the convergence rates of the functional value sequence and corresponding gradient sequence was derived. Techniques to implement the algorithms were discussed. In numerical experiments, those techniques have been successfully implemented to solve for multiple solutions of several quasilinear elliptic boundary value problems and multiple eigenpairs of the well known nonlinear p-Laplacian operator. Numerical solutions were presented by their pro?les for visualization. Several interesting phenomena of the solutions of quasilinear elliptic boundary value problems and the eigenpairs of the p-Laplacian operator have been observed and are open for further investigation. As a generalization of the above results, nonsmooth critical points were considered for locally Lipschitz continuous functionals. A local minmax characterization of nonsmooth saddle critical points was also established. To establish its version in Banach spaces, a new notion, pseudo-generalized-gradient has to be introduced. Based on the characterization, a local minimax algorithm for ?nding multiple nonsmooth saddle critical points was proposed for further study.

The overall purpose of the study was to get a deeper understanding of the process of transition from preschool to compulsory school. According to the purpose the study three issues are the following: 1. How organized the reception to the compulsory school? 2. The motives are to host the compulsory school? 3. What consequences may mean the individual, group and organizational level? The background of the study highlights different factors that influence the transition between pre-school and compulsory school. Also included is a review of research on studies related to students experiences of being in compulsory school and wc alternative solutions which occurred out in the operations, which are relevant for the study. Semi-structured interviews were conducted with eight managers /principals and special educators. The result is divided into four themes. The result in part one includes enrollment processes for compulsory school. Part two describes the reasons for the receipt of compulsory school. The third part shows the impact on the individual group and organizational level. The fourth section deals with children and carers influence and participation. The discussion raised that since the new Education Act (Lgr 11) it is clear who belongs compulsory school and who do not. It requires a diversity of actors that work together to facilitate the transition process for children/ students.

HACCP ( Hazard Analysis and Critical Control Points ) is a science-based system of food safety. This system identifies hazards and risks in food production and it proposes an effective control and monitoring procedures at points that are critical for food safety . In cases where e.g. measured values ( temperature, time) deviates from the set limits are performed specific corrective measures. Within this system of protection of food safety Two critical control points(CCP)were established in selected company and they have been set correctly . Two checkpoints (CP )in HACCP weren´t determined completely so newly designed and in five cases recommended modifications , including one designed to change the compliance time and once in imminent danger .

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-23T12:41:56Z No. of bitstreams: 1 arquivototal.pdf: 3952391 bytes, checksum: 515d42b8a346d93bfff74862f9c40c46 (MD5) / Made available in DSpace on 2017-08-23T12:41:56Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 3952391 bytes, checksum: 515d42b8a346d93bfff74862f9c40c46 (MD5) Previous issue date: 2016-02-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we first study some interesting generalizations of the famous inequality Sobolev to limited domains. Then, we will study the existence of positive solution for a nonlinear elliptic equation on a certain condition Neumann, by imposing certain restricitive condition in the nonlinearity. To we consider more general hypotheses we will assume conditions on the boundary of domain. / Neste trabalho, estudaremos primeiramente algumas generaliza¸c˜oes interessantes da famosa desigualdade de Sobolev para dom´ınios limitados. Em seguida, iremos estudar a existˆencia de solu¸c˜oes positivas para uma equa¸c˜ao el´ıptica n˜ao linear, sob uma certa condi¸c˜ao de Neumann e impondo algumas condi¸c˜oes restritivas sobre a n˜ao linearidade. Para considerarmos hip´oteses mais gerais, assumiremos condi¸c˜oes na fronteira do dom˜Anio.

Diploma thesis focuses on the analysis of critical points in the transport of hazardous materials on the basis of which there is given a methodology for selecting safe routes. Thethesis includes statistical data on the total performance in the transport of hazardous materials within the EU states as well as specifies the proportion of transport performance of hazardous materials to the total performance among the individual European countries. For Czech Republic, the thesis also presents a statistical overview of the accident rate associated with this kind of transport as well as deals with the causes and consequences of the accidents occured during the transportation.