The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Database Rights in Safe European Home: The Path to More Rigorous Protection of Information

1. Introduction "The one that has compiled ... a database, the collection, securing the validity or presentation of which has required an essential investment, has the sole right to control the content over the whole work or over either a qualitatively or quantitatively substantial part of the work both by means of reproduction and by making them available to the public", Finnish Copyright Act, section 49.1 These are the laconic words that implemented the much-awaited and hotly debated European Community Directive on the legal protection of databases,2 the EDD, into Finnish Copyright legislation in 1998. Now in the year 2005, after more than half a decade of the domestic implementation it is yet uncertain as to the proper meaning and construction of the convoluted qualitative criteria the current legislation employs as a prerequisite for the database protection both in Finland and within the European Union. Further, this opaque Pan-European instrument has the potential of bringing about a number of far-reaching economic and cultural ramifications, which have remained largely uncharted or unobserved. Thus the task of understanding this particular and currently peculiarly European new intellectual property regime is twofold: first, to understand the mechanics and functioning of the EDD and second, to realise the potential and risks inherent in the new legislation in economic, cultural and societal dimensions. 2. Subject-matter of the study: basic issues The first part of the task mentioned above is straightforward: questions such as what is meant by the key concepts triggering the functioning of the EDD such as presentation of independent information, what constitutes an essential investment in acquiring data and when the reproduction of a given database reaches either qualitatively or quantitatively the threshold of substantiality before the right-holder of a database can avail himself of the remedies provided by the statutory framework remain unclear and call for a careful analysis. As for second task, it is already obvious that the practical importance of the legal protection providedby the database right is in the rapid increase. The accelerating transformationof information into digital form is an existing fact, not merely a reflection of a shape of things to come in the future. To take a simple example, the digitisation of a map, traditionally in paper format and protected by copyright, can provide the consumer a markedly easier and faster access to the wanted material and the price can be, depending on the current state of the marketplace, cheaper than that of the traditional form or even free by means of public lending libraries providing access to the information online. This also renders it possible for authors and publishers to make available and sell their products to markedly larger, international markets while the production and distribution costs can be kept at minimum due to the new electronic production, marketing and distributionmechanisms to mention a few. The troublesome side is for authors and publishers the vastly enhanced potential for illegal copying by electronic means, producing numerous virtually identical copies at speed. The fear of illegal copying canlead to stark technical protection that in turn can dampen down the demand for information goods and services and furthermore, efficiently hamper the right of access to the materials available lawfully in electronic form and thus weaken the possibility of access to information, education and the cultural heritage of anation or nations, a condition precedent for a functioning democracy. 3. Particular issues in Digital Economy and Information Networks All what is said above applies a fortiori to the databases. As a result of the ubiquity of the Internet and the pending breakthrough of Mobile Internet, peer-to-peer Networks, Localand Wide Local Area Networks, a rapidly increasing amount of information not protected by traditional copyright, such as various lists, catalogues and tables,3previously protected partially by the old section 49 of the Finnish Copyright act are available free or for consideration in the Internet, and by the same token importantly, numerous databases are collected in order to enable the marketing, tendering and selling products and services in above mentioned networks. Databases and the information embedded therein constitutes a pivotal element in virtually any commercial operation including product and service development, scientific research and education. A poignant but not instantaneously an obvious example of this is a database consisting of physical coordinates of a certain selected group of customers for marketing purposes through cellular phones, laptops and several handheld or vehicle-based devices connected online. These practical needs call for answer to a plethora of questions already outlined above: Has thecollection and securing the validity of this information required an essential input? What qualifies as a quantitatively or qualitatively significant investment? According to the Directive, the database comprises works, information and other independent materials, which are arranged in systematic or methodical way andare individually accessible by electronic or other means. Under what circumstances then, are the materials regarded as arranged in systematic or methodical way? Only when the protected elements of a database are established, the question concerning the scope of protection becomes acute. In digital context, the traditional notions of reproduction and making available to the public of digital materials seem to fit ill or lead into interpretations that are at variance with analogous domain as regards the lawful and illegal uses of information. This may well interfere with or rework the way in which the commercial and other operators have to establish themselves and function in the existing value networks of information products and services. 4. International sphere After the expiry of the implementation period for the European Community Directive on legal protection of databases, the goals of the Directive must have been consolidated into the domestic legislations of the current twenty-five Member States within the European Union. On one hand, these fundamental questions readily imply that the problemsrelated to correct construction of the Directive underlying the domestic legislation transpire the national boundaries. On the other hand, the disputes arisingon account of the implementation and interpretation of the Directive on the European level attract significance domestically. Consequently, the guidelines on correct interpretation of the Directive importing the practical, business-oriented solutions may well have application on European level. This underlines the exigency for a thorough analysis on the implications of the meaning and potential scope of Database protection in Finland and the European Union. This position hasto be contrasted with the larger, international sphere, which in early 2005 does differ markedly from European Union stance, directly having a negative effect on international trade particularly in digital content. A particular case in point is the USA, a database producer primus inter pares, not at least yet having aSui Generis database regime or its kin, while both the political and academic discourse on the matter abounds. 5. The objectives of the study The above mentioned background with its several open issues calls for the detailed study of thefollowing questions: -What is a database-at-law and when is a database protected by intellectual property rights, particularly by the European database regime?What is the international situation? -How is a database protected and what is its relation with other intellectual property regimes, particularly in the Digital context? -The opportunities and threats provided by current protection to creators, users and the society as a whole, including the commercial and cultural implications? -The difficult question on relation of the Database protection and protection of factual information as such. 6. Dsiposition The Study, in purporting to analyse and cast light on the questions above, is divided into three mainparts. The first part has the purpose of introducing the political and rationalbackground and subsequent legislative evolution path of the European database protection, reflected against the international backdrop on the issue. An introduction to databases, originally a vehicle of modern computing and information andcommunication technology, is also incorporated. The second part sets out the chosen and existing two-tier model of the database protection, reviewing both itscopyright and Sui Generis right facets in detail together with the emergent application of the machinery in real-life societal and particularly commercial context. Furthermore, a general outline of copyright, relevant in context of copyright databases is provided. For purposes of further comparison, a chapter on the precursor of Sui Generi, database right, the Nordic catalogue rule also ensues. The third and final part analyses the positive and negative impact of the database protection system and attempts to scrutinize the implications further in the future with some caveats and tentative recommendations, in particular as regards the convoluted issue concerning the IPR protection of information per se, a new tenet in the domain of copyright and related rights.

Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Customer reference marketing and utilization of social media as an integral part of customer references

The objective of this Bachelor's Thesis is to find out the role of social media in the B-to-B marketing environment of the information technology industry and to discover how IT-firms utilize social media as a part of their customer reference marketing. To reach the objectives the concepts of customer reference marketing and social media are determined. Customer reference marketing can be characterized as one of the most practically relevant but academically relatively overlooked ways in which a company can leverage its customers and delivered solutions and use them as references in its marketing activities. We will cover which external and internal functions customer references have, that contribute to the growth and performance of B-to-B firms. We also address the three mechanisms of customer reference marketing which are 'status transfer', 'validation through testimonials' and 'demonstration of experience and prior performance'. The concept of social media stands for social interaction and creation of user-based content which exclusively occurs through Internet. The social media are excellent tools for networking because of the fast and easy access, easy interaction and vast amount of multimedia attributes. The allocation of social media is determined. The case company helps clarify the specific characteristics of social media usage as part of customer-reference-marketing activities. For IT-firms the best channels to utilize social media in their customer reference marketing activities are publishing and distribution services of content and networking services.

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Simulation of the Interaction Mean Free Path between Neutrons and TRISO Particles

The interaction mean free path between neutrons and TRISO particles is simulated using scripts written in MATLAB to solve the increasing error present with an increase in the packing factor in the reactor physics code Serpent. Their movement is tracked both in an unbounded and in a bounded space. Their track is calculated, depending on the program, linearly directly using the position vectors of the neutrons and the surface equations of all the fuel particles; by dividing the space in multiple subspaces, each of which contain a fraction of the total number of particles, and choosing the particles from those subspaces through which the neutron passes through; or by choosing the particles that lie within an infinite cylinder formed on the movement axis of the neutron. The estimate from the current analytical model, based on an exponential distribution, for the mean free path, utilized by Serpent, is used as a reference result. The results from the implicit model in Serpent imply a too long mean free path with high packing factors. The received results support this observation by producing, with a packing factor of 17 %, approximately 2.46 % shorter mean free path compared to the reference model. This is supported by the packing factor experienced by the neutron, the simulation of which resulted in a 17.29 % packing factor. It was also observed that the neutrons leaving from the surfaces of the fuel particles, in contrast to those starting inside the moderator, do not follow the exponential distribution. The current model, as it is, is thus not valid in the determination of the free path lengths of the neutrons.

Path Analysis of Online Users Using Clickstream Da-ta: Case Online Magazine Website

This paper explores behavioral patterns of web users on an online magazine web-site. The goal of the study is to first find and visualize user paths within the data generated during collection, and to identify some generic behavioral typologies of user behavior. To form a theoretical foundation for processing data and identifying behavioral ar-chetypes, the study relies on established consumer behavior literature to propose typologies of behavior. For data processing, the study utilizes methodologies of ap-plied cluster analysis and sequential path analysis. Utilizing a dataset of click stream data generated from the real-life clicks of 250 ran-domly selected website visitors over a period of six weeks. Based on the data collect-ed, an exploratory method is followed in order to find and visualize generally occur-ring paths of users on the website. Six distinct behavioral typologies were recog-nized, with the dominant user consuming mainly blog content, as opposed to editori-al content. Most importantly, it was observed that approximately 80% of clicks were of the blog content category, meaning that the majority of web traffic occurring in the site takes place in content other than the desired editorial content pages. The out-come of the study is a set of managerial recommendations for each identified behavioral archetype.