A note to a paper by Ramachandra on transctndental numbers

The thesis deals with the implementation and application of out-of-the-box tools in linear and mixed integer programming. It documents the lessons learned and conclusions drawn from five years of implementing, maintaining, extending, and using several computer codes to solve real-life industrial problems. By means of several examples it is demonstrated how to apply algebraic modeling languages to rapidly devise mathematical models of real-world problems. It is shown that today's MIP solvers are capable of solving the resulting mixed integer programs, leading to an approach that delivers results very quickly. Even though, problems are tackled that not long ago required the implementation of specialized branch-and-cut algorithms. In the first part of the thesis the modeling language Zimpl is introduced. Chapter 2 contains a complete description of the language. In the subsequent chapter details of the implementation are described. Both theoretical and practical considerations are discussed. Aspects of software engineering, error prevention, and detection are addressed. In the second part several real-world projects are examined that employed the methodology and the tools developed in the first part. Chapter 4 presents three projects from the telecommunication industry dealing with facility location problems. Chapter 5 characterizes questions that arise in UMTS planning. Problems, models, and solutions are discussed. Special emphasis is put on the dependency of the precision of the input data and the results. Possible reasons for unexpected and undesirable solutions are explained. Finally, the Steiner tree packing problem in graphs, a well-known hard combinatorial problem, is revisited. A formerly known, but not yet used model is applied to combine switchbox wire routing and via minimization. All instances known from the literature are solved by this approach, as are some newly generated bigger problem instances.

A System Perspective on Business Models

We will show that this construction is impossible if a straightedge and compass are the only tools which we may use. We precede the proof with a couple of definitions and facts which will be needed. A complex number is algebraic if it is a zero of a polynomial with integer coefficients. Numbers which are not algebraic are called transcendental. The set of all algebraic numbers is a field. This implies, in particular, that for any algebraic number a and any natural number k the number ak iS also algebraic. Recall also that each constructible number, i.e., a number which can be constructed using a straightedge and compass only, is algebraic. A crucial result for us is the following theorem due to Lindemann. If x 7s 0 is an algebraic number, then ex is a transcendental number. We refer to [2, 3] for unexplained terminology and details.

Given k ≥ 2 let α1, ..., αk be transcendental numbers such that α1, ..., αk–1 are algebraically independent over Q and αk $\in$ Q(α1, ..., αk–1), but αk, ≠ (aαi + c)/b for some i $\in$ {1, ..., k – 1} and some a, b $\in$ N, c $\in$ Z satisfying gcd(a,b) = 1. We prove that then there exists a nonnegative integer q such that the set of so-called Dirichlet exponents log(n + αj, where n runs through the set of all nonnegative integers for j = 1, ..., k – 1 and n = q, q + 1, q + 2, ... for j = k, is linearly independent over Q. As an application we obtain a joint universality theorem for corresponding Hurwitz zeta functions ζ(s, α1), ..., ζ(s, αk) in the strip {s $\in$ C: 1/2 < $\Re$(s) < 1}. In our approach we follow a recent result of Mishou who analyzed the case k = 2.

The real quaternions algebra was invented by W.R. Hamilton as an extension to the complex numbers. In this paper, we study various kinds of quaternions and investigate some of basic algebraic properties and geometric applications of them.

Electron accelerators have a wide range of applications in basic research, medicine and industry. In order to reduce costs and size of future devices and facilities, advanced compact accelerator concepts are subject to extensive research and development efforts in accelerator physics. A promising approach is the dielectric laser accelerator (DLA). The electromagnetic near-fields of an ultra-short laser pulse scattered by a dielectric structure are used to accelerate electrons. Dielectrics increases the achievable accelerating gradient by a factor of at least 10 in comparison to metallic structures. Recent progress in the development of femtosecond lasers and lithographic techniques in semiconductor fabrication has paved the way to experimental demonstration of DLAs in 2013. Possible applications of DLAs are in attosecond science, in ultrafast electron-microscopy and -diffraction, and in providing relativistic electrons for lithography and radiotherapy. The use of near-fields in structures with period lengths in the order of micrometers leads to complicated particle dynamics during acceleration. Theoretical descriptions of the electromagnetic fields and the resulting particle dynamics are presented in this thesis. In order to confine the particles in the accelerating structures, a focusing scheme is introduced which is adapted from ion accelerators. This allows to transport particles through a DLA structure of arbitrary length. Due to non-linear dynamics of the accelerated electrons, the particle trajectories are calculated numerically. A simulation tool based on the analytical description of the electromagnetic fields in the structures is implemented. Since DLA structures are quasiperiodic, the description simplifies to one complex number per structure period, i.e., the spatial harmonic of the synchronous accelerating mode. The required computational effort is thus significantly reduced as compared to the full electromagnetic fields. Many applications of DLAs require particle distributions of high charge. The beam dynamics are additionally affected by wake fields, which are generated by the interaction of the charge distribution ensemble with the dielectric structures. Detailed studies of wake fields in DLA structures are discussed in this thesis. Moreover, first measurements of energy spectrum modulations caused by wake fields are presented. The wake field effects can lead to instabilities. For the analysis of possible instabilities, wake fields are integrated in the aforementioned numerical simulation tool. This extended tool is applied to compare particle dynamics with simplified analytical models of longitudinal and transverse wake effects and instabilities. These studies provide estimates for the maximum attainable charges of an accelerated particle bunch. For higher bunch charges, the effects from the wake fields exceed the accelerating and focusing laser fields and thus lead to beam loss. Finally, a possible damping mechanism is presented in order to counteract the instabilities and increase the bunch charge limits.

In this paper, we develop the theory of global distributions (i.e. distributions of global fields) and apply it to the study of special values of abelian L-functions of a number field and division points of rank one Drinfeld modules. We introduce the concept of \epsilon-distributions and give examples by \epsilon-partial zeta functions. We determine the ranks of level groups of various kinds of universal distributions of a global field k, such as universal \epsilon-, punctured, punctured even and odd distributions of k. We show the universality of several distributions derived from special values of the \epsilon-partial zeta functions by studying \mathbb{Q}-linear independence of some special values. We also propose a conjecture and a question about the universality of \epsilon-distributions of special values of \epsilon-partial zeta functions.

Despite the importance of the strategic choices taken by subsidiary managers to the long terms survival of their unit, little is known about the phenomenon. (Dörrenbächer &amp; Geppert, 2009, Scott, Gibbons, &amp; Coughlan, 2010). This paper analyses and synthesises the research streams on subsidiary management to date to provide critical conceptual insights and proposes a new theoretical approach to subsidiary analysis, applied to the critical routine of subsidiary strategy. The adoption of more global business structures by MNEs has led to additional strategic constraints on subsidiary managers (Buckley, 2009, Buckley &amp; Ghauri, 2004, Mudambi, 2008), which we categorise as the dual embeddedness constraint, the domain constraint and the resource constraint. Paradoxically despite these exacerbating constraints, expectations on subsidiary managers to create knowledge and innovation and develop their mandate are escalating, forcing them to evaluate the range of strategic decisions remaining under their control, While the literature implicitly assumes that subsidiary managers can respond to MNC pressures by reconfiguring resources and developing capabilities (Birkinshaw &amp; Hood, 1998), improving performance (Subramaniam &amp; Watson, 2006) and influencing the strategic direction of the MNE as a whole (Andersson, Bjorkman, &amp; Forsgren, 2005, Williams, 2009), there is an absence of guidance on how subsidiary managers develop strategies to achieve these options, and influence strategy from below (Andersson, Forsgren, &amp; Holm, 2007). Our review of the empirical and theoretical research on subsidiary management identifies how the tensions between the headquarters perspective and the subsidiary perspective have resulted in the application of inappropriate conceptual frameworks. Platforming from the four primary theoretical approaches applied to date, and combining critical tenets of both the resourced based and transaction cost approaches, we develop a conceptual framework which overcomes prior theoretical limitations and offers a new perspective of subsidiary to apply to the subsidiary unit of analysis.

This research paper for medical science is applying new original further science aimed at curing the Ebola virus and adding to research for the vaccination, curing and treatment of diseases. This research approach achieves the construction of own research from accumulating answers to set goals finding answers to analysis of information of factors associated to disease research and this research adds to medical development needs as observed by actions reported from sources in the news media and from sources in general medical science literature. New theories are presented that apply to medical science involving disease function, new case types, new reactions for new medications and symptom involvement in illness and health and also a new theory of reactions observed that stop disease spread and accounts for cases survival from diseases called the fill clutter and touch lockdown reaction structure pattern stop of diseases theory is proved and has use in scientific understanding and also for producing vaccines, cures and treatments to disease. This research adds to medical science understanding with correct new understanding and potential new methods that is a correct education that does correct research and correct proposals for finding successful results for correct application as this paper outlines a complete account to aid medical science for development of medical vaccines, cures and treatments to diseases that is a new analytical approach for research and treatment. Introduction Vaccines, cures and treatments are exact to be successful and disable targeted diseases. In vaccinating, curing, and treating diseases each reaction of the body and of a disease is addressed to cover every possibility for assured success this in development including medical trials with observed

Manipulation of the catalyst surface coverage for improved conversion and selectivity substantially requires more frequent flow reversals than the classical reverse flow operation for energy saving does (Chapter 1). 2.A reverse flow reactor should be operated at comparable switching time and residence time in order to manipulate the reactor's selectivity (Chapter 3).3. The concept of reverse flow operation with concentration programming provides an engineering tool to control conversion and selectivity, with three benefits: ammonia feedstock savings, increased ammonia conversion, and increased selectivity to NO; a drawback is the decrease of production rate (Chapter 4).4. The concept of reverse flow operation with reactor side feeding shows a fourfold superior performance: higher conversion of ammonia, higher selectivity to NO, no dead gas volume, and high production rate (Chapter 5).5. Intensification of a university study program must assure that the students' residence time distribution for completing their study follows a plug flow model.6.The concept of periodic reactor operation is natural.7. So called relaxation oscillation occurs when the cycling time period is much less than the system's time constant.However, this is not the case during reverse flow operation when operating the reactor at extremely short cycling time.8. The porosity of a fixed bed can be determined elegantly by a combination of reverse flow operation and cycling of the feed concentration.9. Joint bachelor-master-doctor programs improve the selectivity to master and doctor degrees as well as the productivity of a university.10. Assalamu'alaikum is a time-independent greeting.

This paper explores the complex relationship between media and political systems in the context of the International News Flow, regarding the interdisciplinary research area between media study and International Relations. The focus is on International News Flow interactions and effects upon democratic political systems. The aim is to fill the gap concerning international relations in comparative media analysis literature. Despite using Hallin and Mancini's framework (2004, 2012), the present research does not only apply their typology to test its validity, but it also applies the main International Relations theoretical frameworks that deepen the relationship between media and political systems to shed light on the degree of superimposition between structure-based and content-based frameworks of media systems. The case study is the 2016 failed military coup in Turkey. In particular, in terms of coverage and analysis, the study considers how the newspapers of four countries (Italy, France, Germany and England), which represent the three democracy models of Hallini and Mancini – Mediterranean, Liberal, Corporative plus one that cuts across different models – framed the failed coup attempt in the days following the beginning of the crisis.

This thesis focuses on several aspects of olfactory processing in Drosophila . In chapter I and II, I will discuss how odorants are encoded in the brain. In both insects and mammals, olfactory receptor neurons (ORNs) expressing the same odorant receptor gene converge onto the same glomerulus. This topographical organization segregates incoming odor information into combinatorial maps. One prominent theory suggests that insects and mammals discriminate odors based on these distinct combinatorial spatial codes. I tested the combinatorial coding hypothesis by engineering flies that have only one class of functional ORNs and therefore cannot support combinatorial maps. These files can be taught to discriminate between two odorants that activate the single functional class of ORN and identify an odorant across a range of concentrations, demonstrating that a combinatorial code is not required to support learned odor discrimination. In addition, these data suggest that odorant identity can be encoded as temporal patterns of ORN activity. Behaviors are influenced by motivational states of the animal. Chapter III of this thesis focuses on understanding how motivational states control behavior. Appetitive memory in Drosophila provides an excellent system for such studies because the motivational state of hunger promotes reliance on learned appetitive cues whereas satiety suppresses it. We found that activation of neuropeptide F (dNPF) neurons in fed flies releases appetitive memory performance from satiety-mediated suppression. Through a GAL4 screen, we identified six dopaminergic neurons that are a substrate for dNPF regulation. In satiated flies, these neurons inhibit mushroom body output, thereby suppressing appetitive memory performance. Hunger promotes dNPF release, which blocks the inhibitory dopaminergic neurons. The motivational drive of hunger thus affects behavior through a hierarchical inhibitory control mechanism: satiety inhibits memory performance through a subset of dopaminergic neurons, and hunger promotes appetitive memory retrieval via dNPF-mediated disinhibition of these neurons. The aforementioned studies utilize sophisticated genetic tools for Drosophila. In chapter IV, I will talk about two new genetic tools. We developed a new technique to restrict gene expression to different subsets of mushroom body neurons with unprecedented precision. We also adapted the light-activated adenylyl cyclase (PAC) from Euglena gracilis as a light-inducable cAMP system for Drosophila . This system can be used to induce cAMP synthesis in targeted neurons in live, behaving preparations.

Introduction: The purpose of this study is to measure the cumulative doses and dose-area products exposed in chronic totally occluded coronary (CTO) interventions performed under ultra-low dose radiation procedure. Materials and Methods: 47 patients were included to our study. Three experienced CTO operators and team were performed these procedures, one of whom was working with ALARA principles (Operator Group 1, 31 (66%) patients), the remaining operators were working in standard cine mode (Operator Group 2, 16 (34%) patients). Total fluoroscopy time, number of cineangiographic runs, cumulative dose, the dose area product were reviewed for each procedure. ALARA (As Low As Reasonably Achievable) modifications were used by Operator 1, such as reduced pulse width and exposure dose, filter protection, a longer lines for Y connector, pedaling technical as well as low frame rate. Results: Comparison of total fluoroscopy time and the number of cineangiographic runs were not significant. But, on the other hand, cumulative doses and dose area products were significantly lower for the Operator Group 1 (p<0.001 for both parameters). Mean dose area product of CTO procedures were lower than reference levels in the literature in operator Group1. Conclusion: Besides frame rate and fluoroscopy time, the usage of ALARA principles resulted with low radiation exposure compared with conventional techniques during CTO interventions. All catheterization laboratories should strictly apply ALARA principles.

Adaptive gridding methods are of fundamental importance both for industry and academia. As one of the computing methods, the Boundary Element Method (BEM) is used to simulate problems whose fundamental solutions are available. The method is usually characterised as constant elements BEM or linear elements BEM depending on the type of interpolation used at the elements. Its popularity is steadily growing because of its advantages over other numerical methods most important of which being that it only involves obtaining data at the boundary and computation of the solution in the domain is merely a case of post processing through the use of an identity. This results in the reduction of the problem dimension by unity. Although there is a reduction in dimension when we use BEM, the method usually results in full matrices which can be expensive to solve. This makes the method costly for problems that require very fine grids like those with hot spots as in the example of impressed current cathodic protection systems (ICCP). The BEM is a global method in nature in that the solution in one node depends on the solutions in all the other nodes of the grid. Hence an error in one node can pollute the solution in all the other nodes. In this thesis, we first focus our attention on defining and studying both the local and global errors for the BEM. This is not a completely new study as the literature suggests, however, our approach is different. We use the basic foundations of the the method to define the errors. Since the method is a global method, first we use the interpolation error on each element to define what we have called a sublocal error. Then using the sublocal error we have defined the local error. Understanding the local errors enabled us study the global error. Theoretical and numerical results show that these errors are second order in grid size for both the constant and linear element cases. Then, having explored errors, we study a method for adaptive grid refinement for the BEM. Rather than using a truly nonuniform grid, we present a method called local defect correction (LDC) that is based on local uniform grid refinement. This method is already developed and documented for other numerical methods such as finite difference and finite volume methods but not for BEM. In the LDC method, the discretization on a composite grid is based on a combination of standard discretizations on several uniform grids with different grid sizes that cover different parts of the domain. At least one grid, the uniform global coarse grid, should cover the entire boundary. The size of the global coarse grid is chosen in agreement with the relatively smooth behaviour of the solution outside the hot spots. Then several uniform local fine grids each of which covers only a (small) part of the boundary are used in the hot spots. The grid sizes of the local grids are chosen in agreement with the behaviour of the continuous solution in that part of the boundary. The LDC method is an iterative process whereby a basic global discretisation is improved by local discretisations defined in subdomains. The update of the coarse grid solution is achieved by adding a defect correction term to the right hand side of the coarse grid problem. At each iteration step, the process yields a discrete approximation of the continuous solution on the corresponding composite grid. We have shown how this discretisation can be achieved for the BEM. We apply the discretisation to an academic example to demonstrate its implementation and later show how to use it for an application as the ICCP system. The results show that it is a cheaper method than solving on a truly composite grid and converges in a single step.

If each person within an organized culture and climate is treated as positively as possible, then that person, can push others to offer the organization and its parts the best possible. Inclusion can be seen as a reflection of the culture that prevails both in how teachers learn about teaching and what teaching involves. In addition, the objective of integration is to improve the performance and retention of new teachers, i.e. both to strengthen and prevent the loss of teachers, with the ultimate aim of improving the development and learning of pupils. Through all the literature about the issues relating to organisational culture and integration, their interaction, their association and the fact that they are decisive factors for the professional development of a new teacher. The purpose of this work is to highlight the most important points of on these issues and to establish through quantitative research using a questionnaire in newly appointed teachers, the level at which Greek school units apply the most up-to-date perceptions of them and to confirm the correlation between climate, integration and professional development.