This research presents design techniques for a linear power amplifier with high efficiency in wireless handsets. The power amplifier operates with high efficiency at the saturated output power, maintains high linearity with enhanced efficiency at back-off power levels, and covers a broadband frequency response. The amplifier is thus able to operate in multiple modes (2G/2.5G/3G/4G). The design techniques provide contributions to current research in handset power amplifiers, especially to the converged power amplifier architecture, to reduce the number of power amplifiers within the handset while covering all standards and frequency bands around the globe. Three main areas of interest in power amplifier design are investigated: high power efficiency; high linearity; and broadband frequency response. Multiple techniques for improving the efficiency are investigated with the focus on maintaining linear operation. The research applies a new technique to the handset industry, class-J, to improve the power efficiency while avoiding the practical issues that hinder the typical techniques (class-AB and class-F). Class-J has been implemented using GaN FET in high power applications. To our knowledge, this work provides the first implementation of class-J using GaAs HBT in a handset power amplifier. The research investigates the linearity, and the nature and causes of nonlinearities. Multiple concepts for improving the linearity are presented, such as avoiding odd-degree harmonics, and linearizing the relationship between the output current and the input voltage of the amplifier at the fundamental frequency. The concept of bias depression in HBT transistors is introduced with a bias circuit that reduces the bias-offset effect to improve linearity at high output power. A design methodology is presented for broadband matching networks, including the component loss. The methodology offers a quick and accurate estimation of component values, giving more degrees of freedom to meet the design specifications. It enables a trade-off among high out-of-band attenuation, number/size of components, and power loss within the network. Although the main focus is handset power amplifiers, most of the developed techniques can be applied to a wide range of power amplifiers. / Ph. D.

As the demand for wireless electronics is increasing, more and more gadgets are connected wirelessly and devices are being improved constantly. The need of the new research and development for advance electronics with high performances is the priority. The data transfer rates are improved for faster communication and better efficiency is to reduce the battery consumption in handheld devices. This thesis presents three single-stage power amplifiers (PAs): class-AB, class-F and inverse class-F (class-F-1) at 28 GHz. The PAs have identical input networks: input matching, base DC feed, and base stabilizing networks. At the load side, there is a different load network for each PA. Class-AB PA load network has a single inductor with a parasitic capacitor to create a resonance at 28GHz. Class-F PA load network is composed of a parallel network (one LC tank in series with an inductor) and a series network (one 3f0-resonance LC tank in series with a capacitor) to create a multi-resonance load network. Class-F-1 load network is composed of a parallel network (two LC tank in series with an inductor) and a series network (one 2f0-resonance LC tank in series with a capacitor) to have a multi-resonance network. The main purpose of using multi-resonance load networks in class-F and class-F-1 is to shape the collector currents and voltages in order to achieve the highest efficiency possible. The chosen bias point is VCE=2.3V and ICE~12mA. As the results, class-AB PA achieves the peak PAE of 44%, 15 dBm OP-1dB, >19 dBm Psat , and 10 dB Gp. Class-F PA achieves the peak PAE of 46%, 14.5 dBm OP-1dB, ~18 dBm Psat , and 10 dB Gp. Class-F-1 PA achieves the peak PAE of 45%, 15.1 dBm OP-1dB, >18 dBm Psat , and 10 dB Gp.. In order to compare the linearity performances among three PA classes, a two-tone signal and a modulated signal with different modulation schemes (QPSK, 16QAM, 64QAM, and 256QAM) are applied to the PAs to produce IM3, ACPR, and EVM. After the analysis and comparison on efficiency and linearity, class-F PA gives the highest efficiency but has the worst linearity while class-AB has the best linearity but has the worst efficiency among three. Class-F-1 PA results lies in the middle of two other classes in term of efficiency and linearity. / Master of Science / As the demand for wireless electronics is increasing, more and more gadgets are connected wirelessly and devices are being improved constantly. The data transfer rates are improved for faster communication and better efficiency is to reduce the battery consumption in handheld devices. A power amplifier is a very essential component in many microwave and millimeterwave systems. This thesis presents the designs of three different RF power amplifiers (PAs), which belongs to three different types of PAs: class-AB PA, class-F PA, and inverse class-F (class-F^-1) PA. Each PA is designed to show distinct behaviors at a very high frequency around 28 GHz. Some portions of the designs are very identical among three classes. Three PAs have different circuit portions at the output side, which affect the performances of the PAs. There exists a capacitance from the transistor architecture, so called parasitic capacitance (C_P). In class-AB PA output, a single inductor is used to create a resonance with C_P. In class-F and class-F^-1 PA outputs, the combination of inductors and capacitors results in resonances at fundamental frequency (f₀), second harmonic (2f₀), and third harmonic (3f₀) depending on the impedance requirements of each PA. The main purpose is to shape the voltage and current waveforms in order to obtain the highest performances possible. The voltage and current supplied to the PA are chosen to achieve high power and efficiency at the output of the PAs. The most important parameters in PA design are efficiency and linearity. Efficiency is the effectiveness of the DC power conversion process from supplies into microwave power, which can be expressed as the ratio between output power and supplied DC power. Linearity is a term synonymous with fidelity in an audio amplifier. The term refers to the essential job of an amplifier to increase the power level of an input signal without otherwise altering the content of the signal. After the analysis and comparison on power efficiency and linearity, class-F PA gives the highest efficiency but has the worst linearity while class-AB has the best linearity but has the worst efficiency among three. Class-F^-1 PA results lies in the middle of two other classes in term of efficiency and linearity.

State-of-the-art SiGe BiCMOS technologies leverage the maturity of deep-submicron silicon CMOS processing with bandgap-engineered SiGe HBTs in a single platform that is suitable for a wide variety of high performance and highly-integrated applications (e.g., system-on-chip (SOC), system-in-package (SiP)). Due to their bandgap-engineered base, SiGe HBTs are also naturally suited for cryogenic electronics and have the potential to replace the costly de facto technologies of choice (e.g., Gallium-Arsenide (GaAs) and Indium-Phosphide (InP)) in many cryogenic applications such as radio astronomy. This work investigates the response of mixed-signal circuits (both RF and analog circuits) when operating in extreme environments, in particular, at cryogenic temperatures and in radiation-rich environments. The ultimate goal of this work is to attempt to fill the existing gap in knowledge on the cryogenic and radiation response (both single event transients (SETs) and total ionization dose (TID)) of specific RF and analog circuit blocks (i.e., RF switches and voltage references). The design approach for different RF switch topologies and voltage references circuits are presented. Standalone Field Effect Transistors (FET) and SiGe HBTs test structures were also characterized and the results are provided to aid in the analysis and understanding of the underlying mechanisms that impact the circuits' response. Radiation mitigation strategies to counterbalance the damaging effects are investigated. A comprehensive study on the impact of cryogenic temperatures on the RF linearity of SiGe HBTs fabricated in a new 4th-generation, 90 nm SiGe BiCMOS technology is also presented.

Two-dimensional (2-D) models of electrical resistivity are improved by jointly inverting radiomagnetotelluric (RMT) and direct-current resistivity (DCR) data or by allowing for displacement currents in the inversion of RMT data collected on highly resistive bedrock. Uniqueness and stability of the 2-D models are assessed with a model variance and resolution analysis that allows for the non-linearity of the inverse problem. Model variance and resolution are estimated with a truncated singular value decomposition (TSVD) of the sensitivity matrix. In the computation of model errors, inverse singular values are replaced by non-linear semi-axes and the number of included eigenvectors is increased until a given error threshold is reached. Non-linear error estimates are verified with most-squares inversions. For the obtained truncation levels, model resolution matrices are computed. For RMT data, non-linear error appraisals are smaller than linearized ones. Hence, the consideration of the non-linearity in RMT data leads to reduced model errors or enhanced model resolution. The dielectric effect on RMT data is investigated with a new 2-D forward and inverse code that allows for displacement currents. As compared to the quasi-static approximation, apparent resistivities and phases of the impedance tensor elements are found to be significantly smaller and the vertical magnetic transfer function exhibits more distinct sign reversals. More reliable models of electrical resistivity are obtained from areas with highly resistive bedrock, if displacement currents are allowed for. In contrast, inversions with a quasi-static scheme introduce artefactual structures with extremely low or high resistivities. A smoothness-constrained 2-D joint inversion of RMT and DCR data is presented. The non-linear model variance and resolution analysis is applied to single and joint inverse models. For DCR data, the errors estimated by most-squares inversions are consistently larger than those estimated by the non-linear semi-axes, indicating that DCR models are poorly resolved. Certain areas of the joint inverse models are better resolved than in the single inverse models.

In today's digital world, information and communication technology accounts for 3% and 2% of the global power consumption and CO2 emissions respectively. This alarming figure is on an upward trend, as future telecommunications systems and handsets will become even more power hungry since new services with higher bandwidth requirements emerge as part of the so called 'future internet' paradigm. In addition, the mobile handset industry is tightly coupled to the consumer need for more sophisticated handsets with greater battery lifetime. If we cannot make any significant step to reducing the energy gap between the power hungry requirements of future handsets, and what battery technology can deliver, then market penetration for 4G handsets can be at risk. Therefore, energy conservation must be a design objective at the forefront of any system design from the network layer, to the physical and the microelectronic counterparts. In fact, the energy distribution of a handset device is dominated by the energy consumption of the RF hardware, and in particular the power amplifier design. Power amplifier design is a traditional topic that addresses the design challenge of how to obtain a trade-off between linearity and efficiency in order to avoid the introduction of signal distortion, whilst making best use of the available power resources for amplification. However, the present work goes beyond this by investigating a new line of amplifiers that address the green initiatives, namely green power amplifiers. This research work explores how to use the Doherty technique to promote efficiency enhancement and thus energy saving. Five different topologies of RF power amplifiers have been designed with custom-made signal splitters. The design core of the Doherty technique is based on the combination of a class B, class AB and a class C power amplifier working in synergy; which includes 90-degree 2-way power splitter at the input, quarter wavelength transformer at the output, and a new output power combiner. The frequency range for the amplifiers was designed to operate in the 3.4 - 3.6 GHz frequency band of Europe mobile WiMAX. The experimental results show that 30dBm output power can be achieved with 67% power added efficiency (PAE) for the user terminal, and 45dBm with 66% power added efficiency (PAE) for base stations which marks a 14% and 11% respective improvement over current stateof- the-art, while meeting the power output requirements for mobile WiMAX applications.

No presente trabalho, desenvolve-se um programa computacional para análise de instabilidade de perfis de parede fina por meio do método dos elementos finitos (MEF), com discretização em elementos de casca. Para tal finalidade, utiliza-se uma formulação não-linear geométrica do MEF, com descrição lagrangeana total do equilíbrio, tendo posições nodais e vetores generalizados como variáveis fundamentais da formulação, possibilitando a adoção de lei constitutiva tridimensional completa. Dada a adoção de vetores generalizados ao invés de giros, surge o problema de não unicidade desses vetores nas regiões de encontro entre elementos não coplanares. Para contornar esse problema, desenvolvem-se algumas estratégias de acoplamento que são eficientes e que não comprometem o condicionamento do sistema resultante. Em seguida, introduz-se no programa uma estratégia, baseada na análise linear de instabilidade, que consiste na obtenção de autovalores e autovetores correspondendo, respectivamente, a cargas críticas e modos de instabilidade associados. É realizada uma extensão dessa estratégia para a incorporação da análise não-linear de instabilidade, possibilitando a determinação de pontos críticos ao longo da trajetória de equilíbrio de um ponto da estrutura. Desenvolve-se, também, uma interface gráfica para o programa, para a qual se implementam algoritmos para geração de malha de elementos finitos triangulares e quadrilaterais e se possibilita a aplicação de condições de contorno de forma simples. Por fim, apresentam-se exemplos para validar o código computacional desenvolvido e para explorar as potencialidades do mesmo. A partir desses exemplos, conclui-se que a estratégia proposta e a ferramenta computacional desenvolvida funcionam adequadamente, oferecendo como principal vantagem respostas em geral livres de travamento volumétrico quando comparadas aos resultados provenientes da formulação convencional do MEF, encontrados na literatura. / In the present work, a computational program is developed to perform instability analysis in thin-walled profiles employing the finite element method (FEM), using shell elements. For this purpose, a non-linear geometric formulation of FEM is adopted, with Total Lagrangean description of the equilibrium, having nodal positions and unconstrained vectors as fundamental variables of the formulation, instead of displacements and rotations, making possible the adoption of complete three-dimensional constitutive law. Given the adoption of generalized vectors instead of rotations, the problem arises of the vectors\' non-uniqueness in the regions of connection between non-coplanar shell elements. To overcome this problem, some coupling strategies are developed that are efficient and do not result in ill conditioning of the resulting system of equilibrium equations. Then, a strategy based on buckling analysis is considered in the program, which consists of obtaining eigenvalues and eigenvectors related, respectively, to critical loads and instability modes. An extension of this strategy is developed to consider the nonlinear analysis of instability, making possible to determine critical points along the equilibrium path of a point in the structure. A graphical interface is also developed for the program, for which algorithms are implemented for triangular and quadrilateral finite elements mesh generations and easy boundary conditions assignments. Finally, some examples are presented to validate the developments and to explore the potentialities of the computational tool obtained in the work. From the results, it is possible to conclude that the program works properly, offering as main advantage volumetric responses, in general, free of locking when compared to results using the conventional FEM formulation, as found in the literature.

Aplica-se uma formulação Lagrangeana total do Método dos elementos Finitos (MEF) baseada em posições para obter a resposta dinâmica não linear de risers bidimensionais em contato com o leito do mar. Os elementos finitos adaptados e aplicados nas soluções são de barras curvas de pórtico com cinemática de Reissner. Os risers são estruturas cilíndricas e esbeltas utilizadas na indústria offshore para transportar desde o fundo do mar até a plataforma gases, óleos, minerais ou lodo, entre outros produtos. Na modelagem dessas estruturas, destacam-se três problemas de imediato, são eles: a determinação da catenária inicial da tubulação, o comportamento estrutural após a aplicação de deslocamentos severos no topo do riser quando ancorado à plataforma ou embarcação flutuante e o contato do riser com o leito do mar. Estes problemas resultam ou são agravados pela forte instabilidade presente nessas estruturas em razão da grande relação entre a extensão dos dutos e sua rigidez transversal. Para obter a configuração inicial, três técnicas de penalização foram desenvolvidas e comparadas. A primeira utiliza a redução progressiva da rigidez da seção transversal do riser, a segunda aplica a penalização direta nos deslocamentos nodais do riser e a terceira emprega uma solução dinâmica amortecida com redução progressiva da massa e do amortecimento. As técnicas são comparadas entre si e com resultados das bibliografias. A metodologia desenvolvida para a aplicação de deslocamentos severos no topo do riser é fundamentada na suavização da posição tentativa, através de fórmula empírica baseada na remodelagem de malhas da mecânica dos fluidos. Discretiza-se o solo com molas distribuídas, de comportamento linear e não linear físico, cuja influência nodal é desenvolvida consistentemente. De forma geral a introdução dessas molas é feita através da técnica da penalização da energia potencial total. Descreve-se o comportamento não linear, comumente utilizado para solos coesivos argilosos, com um modelo P-y que considera a penetração inicial, a elevação, assim como a repenetração e alguns ciclos de carregamento e descarregamento delimitados pelas curvas das cargas extremas. Uma técnica de moderação das penalidades é utilizada para auxiliar no problema de contato entre o solo e o riser. Além desses aspectos específicos do trabalho, implementaram-se na formulação do MEF as ações decorrentes de carregamentos de flutuação, peso próprio, forças das correntes do mar e condições de contorno (forças e deslocamentos) devidas às ondas do mar. Realiza-se a integração temporal pelo método clássico de Newmark. A formulação desenvolvida junto com as estratégias implementadas mostram-se adequadas e precisas para o tratamento de risers. / A total Lagrangian Finite Element Method (FEM) formulation based on positions is applied to achieve the static and dynamic responses of two dimensional risers that touch the seabed. The adapted finite elements to model risers are curved frame elements based on the Reissner kinematics. Risers are cylindrical slender structures used in the offshore industry to transport from the underground mineral resources (gas, petroleum, mud etc) to the platforms or vessels. In the analysis of this kind of structure three problems immediately arise, that are: the determination of the initial static position (catenary) of the riser, its dynamic behavior when subjected to severe loads or displacements at the top (floating platforms or vessels) and the interaction among the riser and the seabed. These problems come from or are worsened by the strong instability resulting from the large rate between the extension and the transverse dimension of the riser. In order to solve the initial position three techniques are developed and compared. The first uses a progressive reduction of the transverse stiffness of the riser, the second applies a direct penalization on the nodal displacements of the riser and the third employs a dynamic solution with mass and damping reduction. The achieved results are compared with the ones available in literature. The developed methodology to apply severe displacements at the top of risers is a smoothing procedure of the first trial position, based on a strategy of remeshing used in fluid-structure interaction analysis. The soil (seabed), with linear or non-linear behavior is represented by distributed springs and their nodal influence is consistently developed. In a general way the introduction of these springs is done penalizing the total potential energy function. The non-linear behavior, commonly used for cohesive and clayey soil, is done by a P-y model that takes into account the initial penetration, the elevation, as well as some cyclical loads established by extreme curves. A moderation technique of penalty is used to improve the convergence of the soil-structure interaction process. In addition to these specific aspects of the thesis, there are implemented actions resulting from floating, selfweight, sea streams, and waive forces. The time integration is performed by the Newmark method. Examples reveal that the developed formulation and the proposed strategies are adequate to model submersed risers in contact with the seabed.

O projeto de amplificadores de baixo ruído (LNA) aparenta ser um trabalho simples pelos poucos componentes ativos e passivos que o compõe, porém a alta correlação entre os seus parâmetros de projeto dificulta muito esse trabalho. Esta dissertação apresenta uma proposta para contornar essa dificuldade: o uso de algoritmos metaheurísticos, em particular algoritmos genéticos e simulated annealing. Algoritmos metaheurísticos são técnicas avançadas que emulam princípios físicos ou naturais para resolver problemas com alto grau de complexidade. Esses algoritmos estão emergindo nos últimos anos porque têm mostrado eficiência e eficácia. São feitos neste trabalho os projetos de três LNAs, dois (LNA1 e LNA2) para sistemas com arquitetura homódine (LNA com carga capacitiva) e um (LNA3) para sistemas com arquitetura heteródine (LNA com carga resistiva) utilizando-se algoritmos genéticos e simulated annealing (recozimento simulado). Apresenta-se inicialmente a análise detalhada da configuração escolhida para os projetos (fonte comum cascode com degeneração indutiva FCCDI). A frequência de operação dos LNAs é 1,8 GHz e a fonte de alimentação de 2,0 V. Para o LNA1 e o LNA2 se atingiu uma figura de ruído de 2,8 dB e 3,2 dB, consumo de potência de 6,8 mW e 2,7 mW e ganho de tensão de 22 dB e 24 dB, respectivamente. Para LNA3 se atingiu uma figura de ruído de 3,5 dB, consumo de potência de 7,8 mW e ganho de tensão de 15,5 dB. Os resultados obtidos e comparações feitas com LNAs da literatura demonstram viabilidade e eficácia da aplicação de algoritmos metaheurísticos no projeto de LNA. Neste trabalho utilizaram-se as ferramentas ELDO (simulador de circuitos elétricos), versão 2009.1 patch1 64 bits, ASITIC (para projetar e simular os indutores), versão 03.19.00.0.0.0 e MATLAB (o toolbox fornece os algoritmos metaheurísticos), versão 7.9.0.529 R2009b. Além disso, os projetos foram desenvolvidos na tecnologia CMOS 0,35 m da AMS (Austria Micro Systems). / The design of low noise amplifiers (LNA) seems to be a simple work because the small number of active and passive device that they are composes, nevertheless the high trade off of LNA parameters complicates very much the work. This research presents a proposal to contour act the obstacle: to use metaheuristic algorithms, in special genetic algorithms and simulated annealing. The metaheuristic algorithms are advanced techniques that emulate physics or natural principles to solve problems with high grade of complexity. They have been emerging in the last years because they have shown effectiveness and efficiency. In this dissertation were designed three LNAs using genetic algorithms and simulated annealing: two (LNA1 and LNA2) to homódine architecture (LNA with capacitive load) and one (LNA3) to heteródine architecture (LNA with resistive load). First it is show the detailed analysis of configuration chosen to the designs (common source cascode with inductive degeneration). The operation frequency is 1.8 GHz and power supply is 2.0 V for all LNAs. LNA1 and LNA2 reached a noise figure of 2.8 dB and 3.2 dB, a dissipation power of 6.8 mW and 2.7 mW, and a voltage gain of 22 dB and 24 dB respectively. LNA3 reached 3.5 dB of noise figure, 7.8 mW of dissipation power, and 15.5 dB of voltage gain. The results obtained and the comparisons with LNAs from the literature demonstrate that the metaheuristic algorithms show efficiency and effectiveness in the design of LNA. This study was developed with the help of the tools ELDO (electric circuit simulator) version 2009.1 patch1 64 bits, ASITIC (to design and simulate the inductors) version 03.19.00.0.0.0, and MATLAB (the toolbox provides the metaheuristic algorithms) version 7.9.0.529 R2009b. Furthermore, the designs were developed on CMOS 0.35 AMS (Austria Micro Systems) technology.

Automatic speech recognition (ASR) is one of the most important research areas in the field of speech technology and research. It is also known as the recognition of speech by a machine or, by some artificial intelligence. However, in spite of focused research in this field for the past several decades, robust speech recognition with high reliability has not been achieved as it degrades in presence of speaker variabilities, channel mismatch condi- tions, and in noisy environments. The superb ability of the human auditory system has motivated researchers to include features of human perception in the speech recognition process. This dissertation investigates the roles of perceptual features of human hearing in automatic speech recognition in clean and noisy environments. Methods of simplified synaptic adaptation and two-tone suppression by companding are introduced by temporal processing of speech using a zero-crossing algorithm. It is observed that a high frequency enhancement technique such as synaptic adaptation performs better in stationary Gaussian white noise, whereas a low frequency enhancement technique such as the two-tone sup- pression performs better in non-Gaussian non-stationary noise types. The effects of static compression on ASR parametrization are investigated as observed in the psychoacoustic input/output (I/O) perception curves. A method of frequency dependent asymmetric compression technique, that is, higher compression in the higher frequency regions than the lower frequency regions, is proposed. By asymmetric compression, degradation of the spectral contrast of the low frequency formants due to the added compression is avoided. A novel feature extraction method for ASR based on the auditory processing in the cochlear nucleus is presented. The processings for synchrony detection, average discharge (mean rate) processing and the two tone suppression are segregated and processed separately at the feature extraction level according to the differential processing scheme as observed in the AVCN, PVCN and the DCN, respectively, of the cochlear nucleus. It is further observed that improved ASR performances can be achieved by separating the synchrony detection from the synaptic processing. A time-frequency perceptual spectral subtraction method based on several psychoacoustic properties of human audition is developed and evaluated by an ASR front-end. An auditory masking threshold is determined based on these psychoacoustic e?ects. It is observed that in speech recognition applications, spec- tral subtraction utilizing psychoacoustics may be used for improved performance in noisy conditions. The performance may be further improved if masking of noise by the tonal components is augmented by spectral subtraction in the masked region.

<p>Active vibration control to reduce vibrations and structure borne noise is considered using a powerful multi-disciplinary virtual design environment which enables control system design to be considered as an integral part of the overall vehicle design.</p><p>The main application studied is active automotive engine vibration isolation where, first, the potential of large frequency band multi-input multi-output H₂ feedback control is considered. Facilitated by the virtual environment, it is found necessary to take non-linear characteristics into account to achieve closed-loop stability.</p><p>A physical explanation to why receiver structure flexibility insignificantly affect the open and closed-loop characteristics in case of total force feedback in contrast to acceleration feedback is then given. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed.</p><p>Next, applying state-of-the-art algorithms for recursive parameter estimation, time-domain adaptive filtering is shown to lack sufficient tracking performance to deal with multiple spectral components of transient engine excitations corresponding to rapid car accelerations.</p><p>Finally, plant non-linearity as well as transient excitation are successfully handled using narrow band control based on feedback of disturbance states estimates. To deal with the non-linear characteristics, an approach to generate linear parameter varying descriptions of non-linear systems is proposed. Parameter dependent quadratic stability is assessed using a derived affine closed-loop system representation.</p><p>This thesis also considers actuator saturation induced limit cycles for observer-based state feedback control systems encountered when dealing with the active isolation application. It is stressed that the fundamental observer-based anti-windup technique could imply severely deteriorated closed-loop characteristics and even sustained oscillations. That is in the case when the observer is fed by the saturated control signal in contrast to the computed one. Based on piecewise affine system descriptions, analytical tools to conclude about limit cycles and exponential closed-loop stability are provided for the two observer implementations.</p>