The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Quasi-Regular Solutions for 3D Equations of Tricomi and Keldish Types

Цветан Д. Христов, Недю Ив. Попиванов, Манфред Шнайдер - Изучени са някои тримерни гранични задачи за уравнения от смесен тип. За уравнения от типа на Трикоми те са формулирани от М. Протер през 1952, като тримерни аналози на задачите на Дарбу или Коши–Гурса в равнината. Добре известно е, че новите задачи са некоректни. Ние формулираме нова гранична задача за уравнения от типа на Келдиш и даваме понятие за квазиругулярно решение на тази задача и на eдна от задачите на Протер. Намерени са достатъчни условия за единственост на такива решения.

Spatio-temporal techniques for user identification by means of GPS mobility data

One of the greatest concerns related to the popularity of GPS-enabled devices and applications is the increasing availability of the personal location information generated by them and shared with application and service providers. Moreover, people tend to have regular routines and be characterized by a set of “significant places”, thus making it possible to identify a user from his/her mobility data. In this paper we present a series of techniques for identifying individuals from their GPS movements. More specifically, we study the uniqueness of GPS information for three popular datasets, and we provide a detailed analysis of the discriminatory power of speed, direction and distance of travel. Most importantly, we present a simple yet effective technique for the identification of users from location information that are not included in the original dataset used for training, thus raising important privacy concerns for the management of location datasets.

Some Fixed Point Theorems for Kannan Mappings

2000 Mathematics Subject Classification: Primary: 47H10; Secondary: 54H25.

Inverse space-dependent force problems for the wave equation

The determination of the displacement and the space-dependent force acting on a vibrating structure from measured final or time-average displacement observation is thoroughly investigated. Several aspects related to the existence and uniqueness of a solution of the linear but ill-posed inverse force problems are highlighted. After that, in order to capture the solution a variational formulation is proposed and the gradient of the least-squares functional that is minimized is rigorously and explicitly derived. Numerical results obtained using the Landweber method and the conjugate gradient method are presented and discussed illustrating the convergence of the iterative procedures for exact input data. Furthermore, for noisy data the semi-convergence phenomenon appears, as expected, and stability is restored by stopping the iterations according to the discrepancy principle criterion once the residual becomes close to the amount of noise. The present investigation will be significant to researchers concerned with wave propagation and control of vibrating structures.

Exact solution for the energy spectrum of Kelvin-wave turbulence in superfluids

We study the statistical and dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the dynamical equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.

Every hierarchy of beliefs is a type

When modeling game situations of incomplete information one usually considers the players’ hierarchies of beliefs, a source of all sorts of complications. Harsányi (1967-68)’s idea henceforth referred to as the ”Harsányi program” is that hierarchies of beliefs can be replaced by ”types”. The types constitute the ”type space”. In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.

Az exportteljesítmények és a hátterükben álló vállalati jellemzők elemzése (Export performance clusters of the Hungarian enterprises)

A tanulmány célja a Magyarországon működő exportáló vállalatok jellemzőinek feltárása volt a 2009-es vállalati versenyképességi felmérés alapján. Több tanulmány vizsgálta a vállalatok exportteljesítményét vállalati méret és tulajdonosi szerkezet szerinti bontásban, az elemzésben a szerző viszont ettől eltérő szemléletmódot alkalmazott. A vállalatok exportteljesítménye áll (exportértékesítés volumene, aránya, exportárbevétel változása, jövedelmezőség), a vállalati csoportképzés, klaszterelemzés középpontjában. Három jól elkülöníthető klasztert sikerült azonosítani: a jelentős exporthányaddal és folyamatos növekedéssel jellemezhető sikeres exportáló vállalatok csoportját, a stagnálással, s gyakran csökkenő exportértékesítéssel jellemezhető vállalatcsoportot, s végül a harmadik klasztert azok a jelenleg még alacsony export-ár bevétellel és alacsony exportaránnyal jellemezhető vállalatok képezték, melyekre a növekedés és a kiugróan magas jövedelmezőség volt a jellemző. Az elemzés egyediségét az adja, hogy a vállalati versenyképességi felmérés adatbázisa lehetővé tette a különböző exportteljesítmények hátterében álló működési jellemzők vizsgálatát, amelynek eredményeit a cikk bemutatja. Fő következtetésként megállapítható, hogy a sikeres exportáló vállalatok csoportja mindegyik jellemző szerint jobb működési jellemzőkkel rendelkezik a másik két csoporthoz viszonyítva. / === / The purpose of the paper is to reveal the main characteristics of the Hungarian export oriented firms. It is based on the Hungarian Competitiveness Research Survey 2009. 85% of enterprises were small or medium size in the sample. The aim of the analysis was to identify main factors and tendencies of the overall export performance. Several papers discussed the export activities of firms according to their size and ownership structure in Hungary. A different method was used here. The overall export performance (measured by volume, change, and share of export revenues, and firm profitability ratios) was put in the centre of cluster analysis. Three different clusters were identified. Firms in the firstcluster had significant export performance and growth rate. The second cluster was the group of stagnating firms and the third one contained those whose export performance was low but signaled growth with excellent profitability ratios. The uniqueness of the paper derived from the Competitiveness Research Survey because it provided an opportunity to analyse the connection between export performance and other management and operational characteristics of enterprises. The paper may induce futher research in exploring main enterprise level factors of export performance of the Hungarian firms.

On optimal completions of incomplete pairwise comparison matrices

An important variant of a key problem for multi-attribute decision making is considered. We study the extension of the pairwise comparison matrix to the case when only partial information is available: for some pairs no comparison is given. It is natural to define the inconsistency of a partially filled matrix as the inconsistency of its best, completely filled completion. We study here the uniqueness problem of the best completion for two weighting methods, the Eigen-vector Method and the Logarithmic Least Squares Method. In both settings we obtain the same simple graph theoretic characterization of the uniqueness. The optimal completion will be unique if and only if the graph associated with the partially defined matrix is connected. Some numerical experiences are discussed at the end of the paper.

A method for solving LSM problems of small size in the AHP

The Analytic Hierarchy Process (AHP) is one of the most popular methods used in Multi-Attribute Decision Making. It provides with ratio-scale measurements of the prioirities of elements on the various leveles of a hierarchy. These priorities are obtained through the pairwise comparisons of elements on one level with reference to each element on the immediate higher level. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM), Logarithmic Least Squares Method (LLSM), Weighted Least Squares Method (WLSM) and Chi Squares Method (X2M) are of the tools for computing the priorities of the alternatives. This paper studies a method for generating all the solutions of the LSM problems for 3 × 3 matrices. We observe non-uniqueness and rank reversals by presenting numerical results.

Jerash: The landscape, urban space, and architecture

The peculiarities of Roman architecture, town planning, and landscape architecture are visible in many of the empire's remaining cities. However, evaluation of the landscapes; and analysis of the urban fabric, spatial compositions, and the concepts and characteristics of its open spaces are missing for Jerash (Gerasa in antiquity) in Jordan. Those missing elements will be discussed in this work, as an example of an urban arrangement that survived through different civilizations in history.^ To address the characteristics of the exterior spaces in Jerash, a study of the major concepts of planning in Classical Antiquity will be conducted, followed by a comparative analysis of the quality of space and architectural composition in Jerash. Through intensive investigation of data available for the area under study, the historical method used in this paper illustrates the uniqueness of the site's urban morphology and architectural disposition.^ An analysis will be performed to compare the design composition of the landscape, urban fabric, and open space of Jerash as a provincial Roman city with its existing excavated remains. Such an analysis will provide new information about the roles these factors and their relationships played in determining the design layout of the city. Information, such as the relationship between void and solid, space shaping, the ground and ceiling, the composition of city elements, the ancient landscapes, and the relationship between the land and architecture, will be acquired.^ A computer simulation for a portion of the city will be developed to enable researchers, students and citizens interested in Jordan's past to visualize more clearly what the city looked like in its prime. Such a simulation could result in the revival of the old city of Jerash and help promote its tourism. ^

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Eden in the age of the fifth sun: The narrative work of Homero Aridjis

Homero Aridjis (b. 1940) is a major Mexican poet, novelist, essayist and ecological activist whose prolific body of work, ranging over forty years and including more than eleven volumes of poetry and thirteen novels, has yet to be studied as a coherent literary corpus in the context of recent Latin American fiction. The purpose of this dissertation was to analyze the narrative works of this author as both illustrative of the changes that have occurred in Latin American fiction since the 1960s when it first burst onto the world scene, as well as to study the uniqueness of this particular author's view of literature as it relates to historical discourse, apocalypticism. and social commitment. ^ Research showed that in the case of the narrative style of Aridjis, major trends in the contemporary Latin American novel were present in such a profuse and model manner as to confirm this author's importance as a prime example of what is commonly known as “Post-Boom” fiction. However, beyond the mere presence of literary elements, this study showed that the author's unique approach to narrative style has altered and expanded the aesthetic and thematic possibilities of the contemporary novel. The area where this is most clearly seen is in his experimentation with the historical genre. By manipulating the referential techniques of what has lately come to be known as the “new historical novel,” Aridjis has written both a cycle of purely historical novels and a cycle of futuristic ones that attempt to transcend the temporal limits traditionally imposed by these narrative forms, fusing them into one constant questioning of the nature of love, hate and identity. In this manner, he has developed a “simultaneist” narrative approach where distinct historical and imagined periods, places, people, things, and texts coexist and interact, widening almost to delirium the interpretative possibilities of the work. ^ This unique view of time and narrative, together with the author's political activism and millenarian view of history, make the novels of Homero Aridjis an important element in understanding the continuing development and evolution of Latin American fiction at the turn of the century. ^

Three-dimensional brain fiber tracking modeling in diffusion tensor imaging

This dissertation establishes the foundation for a new 3-D visual interface integrating Magnetic Resonance Imaging (MRI) to Diffusion Tensor Imaging (DTI). The need for such an interface is critical for understanding brain dynamics, and for providing more accurate diagnosis of key brain dysfunctions in terms of neuronal connectivity. ^ This work involved two research fronts: (1) the development of new image processing and visualization techniques in order to accurately establish relational positioning of neuronal fiber tracts and key landmarks in 3-D brain atlases, and (2) the obligation to address the computational requirements such that the processing time is within the practical bounds of clinical settings. The system was evaluated using data from thirty patients and volunteers with the Brain Institute at Miami Children's Hospital. ^ Innovative visualization mechanisms allow for the first time white matter fiber tracts to be displayed alongside key anatomical structures within accurately registered 3-D semi-transparent images of the brain. ^ The segmentation algorithm is based on the calculation of mathematically-tuned thresholds and region-detection modules. The uniqueness of the algorithm is in its ability to perform fast and accurate segmentation of the ventricles. In contrast to the manual selection of the ventricles, which averaged over 12 minutes, the segmentation algorithm averaged less than 10 seconds in its execution. ^ The registration algorithm established searches and compares MR with DT images of the same subject, where derived correlation measures quantify the resulting accuracy. Overall, the images were 27% more correlated after registration, while an average of 1.5 seconds is all it took to execute the processes of registration, interpolation, and re-slicing of the images all at the same time and in all the given dimensions. ^ This interface was fully embedded into a fiber-tracking software system in order to establish an optimal research environment. This highly integrated 3-D visualization system reached a practical level that makes it ready for clinical deployment. ^

Space division multiple access for wireless sensor networks

This dissertation proposed a self-organizing medium access control protocol (MAC) for wireless sensor networks (WSNs). The proposed MAC protocol, space division multiple access (SDMA), relies on sensor node position information and provides sensor nodes access to the wireless channel based on their spatial locations. SDMA divides a geographical area into space divisions, where there is one-to-one map between the space divisions and the time slots. Therefore, the MAC protocol requirement is the sensor node information of its position and a prior knowledge of the one-to-one mapping function. The scheme is scalable, self-maintaining, and self-starting. It provides collision-free access to the wireless channel for the sensor nodes thereby, guarantees delay-bounded communication in real time for delay sensitive applications. This work was divided into two parts: the first part involved the design of the mapping function to map the space divisions to the time slots. The mapping function is based on a uniform Latin square. A Uniform Latin square of order k = m 2 is an k x k square matrix that consists of k symbols from 0 to k-1 such that no symbol appears more than once in any row, in any column, or in any m x in area of main subsquares. The uniqueness of each symbol in the main subsquares presents very attractive characteristic in applying a uniform Latin square to time slot allocation problem in WSNs. The second part of this research involved designing a GPS free positioning system for position information. The system is called time and power based localization scheme (TPLS). TPLS is based on time difference of arrival (TDoA) and received signal strength (RSS) using radio frequency and ultrasonic signals to measure and detect the range differences from a sensor node to three anchor nodes. TPLS requires low computation overhead and no time synchronization, as the location estimation algorithm involved only a simple algebraic operation.