Hyperbolic Fourth-R Quadratic Equation and Holomorphic Fourth-R Polynomials

MSC 2010: 30C10, 32A30, 30G35

Integral Representations of Functional Series with Members Containing Jacobi Polynomials

MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

WDM orthogonal subcarrier multiplexing

Electro-optical transceivers can be implemented employing all-analog signal processing in order to achieve low values of power consumption and latency. This paper shows that the spectral efficiency of such solutions can be increased by combining orthogonal multicarrier techniques and off-the-shelf microwave components. A real-time 108-Gbit/s experiment was performed emulating a wavelength division multiplexing (WDM) system composed of five optical channels. The optical carriers were provided by an externally injected gain switched optical frequency comb. Each optical channel transmitted a 21.6-Gbit/s orthogonal subcarrier multiplexing (SCM) signal that was modulated and demodulated in the electrical domain without the requirement for digital signal processing. The net data rate remained higher than 100 Gbit/s after taking into account forward error correction overheads. The use of orthogonally overlapping subchannels achieves an unprecedented spectral efficiency in all-analog real-time broadband WDM/SCM links.

Orthogonal frequency division multiplexing based air interfaces and multiple input multiple output techniques in cooperative satellite communications for 4th generation mobile systems

Recently, wireless network technology has grown at such a pace that scientific research has become a practical reality in a very short time span. Mobile wireless communications have witnessed the adoption of several generations, each of them complementing and improving the former. One mobile system that features high data rates and open network architecture is 4G. Currently, the research community and industry, in the field of wireless networks, are working on possible choices for solutions in the 4G system. 4G is a collection of technologies and standards that will allow a range of ubiquitous computing and wireless communication architectures. The researcher considers one of the most important characteristics of future 4G mobile systems the ability to guarantee reliable communications from 100 Mbps, in high mobility links, to as high as 1 Gbps for low mobility users, in addition to high efficiency in the spectrum usage. On mobile wireless communications networks, one important factor is the coverage of large geographical areas. In 4G systems, a hybrid satellite/terrestrial network is crucial to providing users with coverage wherever needed. Subscribers thus require a reliable satellite link to access their services when they are in remote locations, where a terrestrial infrastructure is unavailable. Thus, they must rely upon satellite coverage. Good modulation and access technique are also required in order to transmit high data rates over satellite links to mobile users. This technique must adapt to the characteristics of the satellite channel and also be efficient in the use of allocated bandwidth. Satellite links are fading channels, when used by mobile users. Some measures designed to approach these fading environments make use of: (1) spatial diversity (two receive antenna configuration); (2) time diversity (channel interleaver/spreading techniques); and (3) upper layer FEC. The author proposes the use of OFDM (Orthogonal Frequency Multiple Access) for the satellite link by increasing the time diversity. This technique will allow for an increase of the data rate, as primarily required by multimedia applications, and will also optimally use the available bandwidth. In addition, this dissertation approaches the use of Cooperative Satellite Communications for hybrid satellite/terrestrial networks. By using this technique, the satellite coverage can be extended to areas where there is no direct link to the satellite. For this purpose, a good channel model is necessary.

Racioethnic differences in job satisfaction: A test of orthogonal cultural identification theory and self -categorization theory

The theories of orthogonal cultural identification and self-categorization are offered as links in examining the possible racioethnic differences in job satisfaction. It is posited that racioethnicity (Cox & Blake, 1991) is multidimensional with at least three conceptually distinct dimensions. Since there is a need for consistent terminology with respect to these distinct dimensions, the following new terms are offered to differentiate among them: "physioethnicity" refers to the physiological dimension of racioethnicity; "socioethnicity" refers to the sociocultural dimension; and "psychoethnicity" refers to the psychological dimension.^ Results showed that for the dominant group (Hispanics in this case) (1) bicultural and multicultural individuals were more satisfied with coworkers than acultural and monocultural individuals and (2) individuals with higher strength of psychoethnicity were more satisfied with coworkers, the work itself, and supervision than those with lower strength of psychoethnicity. The findings suggest racioethnic differences within the dominant group and between groups beyond race. ^

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC's minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats.

Orthogonal Frequency Division Multiplexing Based Air Interfaces and Multiple Input Multiple Output Techniques in Cooperative Satellite Communications for 4th Generation Mobile Systems

Recently, wireless network technology has grown at such a pace that scientific research has become a practical reality in a very short time span. One mobile system that features high data rates and open network architecture is 4G. Currently, the research community and industry, in the field of wireless networks, are working on possible choices for solutions in the 4G system. The researcher considers one of the most important characteristics of future 4G mobile systems the ability to guarantee reliable communications at high data rates, in addition to high efficiency in the spectrum usage. On mobile wireless communication networks, one important factor is the coverage of large geographical areas. In 4G systems, a hybrid satellite/terrestrial network is crucial to providing users with coverage wherever needed. Subscribers thus require a reliable satellite link to access their services when they are in remote locations where a terrestrial infrastructure is unavailable. The results show that good modulation and access technique are also required in order to transmit high data rates over satellite links to mobile users. The dissertation proposes the use of OFDM (Orthogonal Frequency Multiple Access) for the satellite link by increasing the time diversity. This technique will allow for an increase of the data rate, as primarily required by multimedia applications, and will also optimally use the available bandwidth. In addition, this dissertation approaches the use of Cooperative Satellite Communications for hybrid satellite/terrestrial networks. By using this technique, the satellite coverage can be extended to areas where there is no direct link to the satellite. The issue of Cooperative Satellite Communications is solved through a new algorithm that forwards the received data from the fixed node to the mobile node. This algorithm is very efficient because it does not allow unnecessary transmissions and is based on signal to noise ratio (SNR) measures.

Um estudo sobre polinômios matriciais

This research work aims to make a study of the algebraic theory of matrix monic polynomials, as well as the definitions, concepts and properties with respect to block eigenvalues, block eigenvectors and solvents of P(X). We investigte the main relations between the matrix polynomial and the Companion and Vandermonde matrices. We study the construction of matrix polynomials with certain solvents and the extention of the Power Method, to calculate block eigenvalues and solvents of P(X). Through the relationship between the dominant block eigenvalue of the Companion matrix and the dominant solvent of P(X) it is possible to obtain the convergence of the algorithm for the dominant solvent of the matrix polynomial. We illustrate with numerical examples for diferent cases of convergence.

Comparing the orthogonal and homotopy functor calculi

Goodwillie’s homotopy functor calculus constructs a Taylor tower of approximations toF , often a functor from spaces to spaces. Weiss’s orthogonal calculus provides a Taylortower for functors from vector spaces to spaces. In particular, there is a Weiss towerassociated to the functor V ÞÑ FpSVq, where SVis the one-point compactification of V .In this paper, we give a comparison of these two towers and show that when F isanalytic the towers agree up to weak equivalence. We include two main applications, oneof which gives as a corollary the convergence of the Weiss Taylor tower of BO. We alsolift the homotopy level tower comparison to a commutative diagram of Quillen functors,relating model categories for Goodwillie calculus and model categories for the orthogonal calculus.

An energy based force prediction method for UD-CFRP orthogonal machining

The machining of carbon fiber reinforced polymer (CFRP) composite presents a significant challenge to the industry, and a better understanding of machining mechanism is the essential fundament to enhance the machining quality. In this study, a new energy based analytical method was developed to predict the cutting forces in orthogonal machining of unidirectional CFRP with fiber orientations ranging from 0° to 75°. The subsurface damage in cutting was also considered. Thus, the total specific energy for cutting has been estimated along with the energy consumed for forming new surfaces, friction, fracture in chip formation and subsurface debonding. Experiments were conducted to verify the validity of the proposed model.

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Database evolution on an orthogonal persistent programming system: A semi-transparent approach

In this paper the problem of the evolution of an object-oriented database in the context of orthogonal persistent programming systems is addressed. We have observed two characteristics in that type of systems that offer particular conditions to implement the evolution in a semi-transparent fashion. That transparency can further be enhanced with the obliviousness provided by the Aspect-Oriented Programming techniques. Was conceived a meta-model and developed a prototype to test the feasibility of our approach. The system allows programs, written to a schema, access semi-transparently to data in other versions of the schema.

Orthogonal chirp division multiplexing for coherent optical fiber communications

In this paper, we propose an orthogonal chirp division multiplexing (OCDM) technique for coherent optical communication. OCDM is the principle of orthogonally multiplexing a group of linear chirped waveforms for high-speed data communication, achieving the maximum spectral efficiency (SE) for chirp spread spectrum, in a similar way as the orthogonal frequency division multiplexing (OFDM) does for frequency division multiplexing. In the coherent optical (CO)-OCDM, Fresnel transform formulates the synthesis of the orthogonal chirps; discrete Fresnel transform (DFnT) realizes the CO-OCDM in the digital domain. As both the Fresnel and Fourier transforms are trigonometric transforms, the CO-OCDM can be easily integrated into the existing CO-OFDM systems. Analyses and numerical results are provided to investigate the transmission of CO-OCDM signals over optical fibers. Moreover, experiments of 36-Gbit/s CO-OCDM signal are carried out to validate the feasibility and confirm the analyses. It is shown that the CO-OCDM can effectively compensate the dispersion and is more resilient to fading and noise impairment than OFDM.

Influence of the cutting edge micro-geometry of PCBN tools on the flank wear in orthogonal quenched and tempered turning M2 steel

Quenched and tempered high-speed steels obtained by powder metallurgy are commonly used in automotive components, such as valve seats of combustion engines. In order to machine these components, tools with high wear resistance and appropriate cutting edge geometry are required. This work aims to investigate the influence of the edge preparation of polycrystalline cubic boron nitride (PCBN) tools on the wear behavior in the orthogonal longitudinal turning of quenched and tempered M2 high-speed steels obtained by powder metallurgy. For this research, PCBN tools with high and low-CBN content have been used. Two different cutting edge geometries with a honed radius were tested: with a ground land (S shape) and without it (E shape). Also, the cutting speed was varied from 100 to 220 m/min. A rigid CNC lathe was used. The results showed that the high-CBN, E-shaped tool presented the longest life for a cutting speed of 100 m/min. High-CBN tools with a ground land and honed edge radius (S shaped) showed edge damage and lower values of the tool’s life. Low-CBN, S-shaped tools showed similar results, but with an inferior performance when compared with tools with high CBN content in both forms of edge preparation.