A passive wireless surface acoustic wave sensor of a delay-line type is composed of an antenna, a transducer that converts the EM signal into a surface acoustic wave, and a set of acoustic reflectors that reflect the incoming signal back out through the antenna. A cavity forms between the transducer and the reflectors, trapping energy and causing multiple unwanted echoes. The work in this dissertation aims to reduce the unwanted echoes so that only the main transit signal is left--the signal of interest with sensor information. The contributions of this dissertation include reflective delay-line device response in the form of an infinite impulse response (IIR) filter. This may be used in the future to subtract out unwanted echoes via post-processing. However, this dissertation will use a physical approach to echo suppression by using a unidirectional transducer. Thus a unidirectional transducer is used and also optimized for 3rd harmonic operation. Both the directionality and the coupling of the 3rd harmonic optimized SPUDT are improved over a standard electrode width controlled (EWC) SPUDT. New type of reflectors for the reflective delay-line device are also presented. These use BPSK type coding, similar to that of the Walsh-Hadamard codes. Two types are presented, variable reflectivity and variable chip-lengths. The COM model is used to simulate devices and compare the predicted echo suppression level to that of fabricated devices. Finally, a device is mounted on a tunable antenna and the echo is suppressed on a wireless operating device.

The progess in NMRQIP can be outlined in to four parts.1) Implementation of theoretical protocols on small number of qubits. 2) Demonstration of QIP on various NMR systems. 3) Designing and implementing the algorithms for mixed initial states. 4) Developing the techniques for coherent and decoherent control on higher number(up to 15) of qubits. This thesis contains some efforts in the direction of first three points. Quantum-state discrimination has important applications in the context of quantum communication and quantum cryptography. One of the characteristic features of quantum mechanics is that it is impossible to devise a measurement that can distinguish nonorthogonal states perfectly. However, one can distinguish them with a finite probability by an appropriate measurement strategy. In Chapter 2, we describe the implementation of a theoretical protocol of programmable quantum-state discriminator, on a two-qubit NMR System. The projective measurement is simulated by adding two experiments. This device does the unambiguous discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and eillipitically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla quubit. The last step of any QIP protocol is the readout. In NMR-QIP the readout is done by using density matrix tomography. It was first proposed by Ernst and co-workers that a two-dimensional method can be used to correlate input and output states. This method uses an extra (aniclla) qubit, whose transitions indicate the quantum states of the remaining qubits. The 2D spectrum of ancilla qubit represent the input and output states along F1 and F2 dimensions respectively. However the 2D method requires several t1 increments to achieve the required spectral width and resolution in the indirect dimension, hence leads to large experimental time. In chapter 3, the conventional 2D NMRQIP method is speeded-up by using Hadamard spectroscopy. The Hadamard method is used to implement various two-, three-qubit gates and qutrit gates. We also use Hadamard spectroscopy for information storage under spatial encoding and to implement a parallel search algorithm. Various slices of water sample can be spatially encoded by using a multi-frequency pulse under the field gradient. Thus the information of each slice is projected to the frequency space. Each slice represents a classical bit, where excitation and no excitation corresponds to the binary values 0 and 1 respectively. However one has to do the experiment for each binary information, by synthesizing a suitable multi-frequency pulse. In this work we show that by recording the data obtained by various Hadamard encoded multi-frequency pulses, one can suitably decode it to obtain any birnary information, without doing further experiments. Geometric phases depend only on the geometry of the path executed in the projective Hilbert space, and are therefore resilient to certain types of errors. This leads to the possibility of an intrinsically fault-tolerant quantum computation. In liquid state NMRQIP. Controlled phase shift gates are achieved by using qubit selective pulses and J evolutions, and also by using geometir phases. In order to achieve higher number of qubits in NMR, one explores dipolar couplings which are larger in magnitude, yielding strongly coupled spectra. In such systems since the Hamiltonian consists of terms, it is difficult to apply qubit selective pulses. However such systems have been used for NMRQIP by considering 2n eigen states as basis states of an n-qubit system. In chapter 4, it is shown that non-adiabatic geometric phases can be used to implement controlled phase shift gates in strongly dipolar coupled systems. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Using such controlled phase shift gates, the implementation of Deutsch-Jozsa and parity algorithms are demonstrated. Search algorithms play an important role in the filed of information processing. Grovers quantum search algorithm achieves polynomial speed-up over the classical search algorithm. Bruschweiler proposed a Liouville space search algorithm which achieve polymonial speed-up. This algorithm requires a weakly coupled system with a mixed initial state. In chapter 5 we modified the Bruschweiler’s algorithm, so that it can be implemented on a weakly as well as strongly coupled system. The experiments are performed on a strongly dipolar coupled four-qubit system. The experiments from four spin-1/2 nuclei of a molecule oriented in a liquid crystal matrix. Chapter 6 describes the implementation of controlled phase shift gates on a quadrupolar spin-7/2 nucleus, using non-adiabatic geometric phases. The eight energy levels of spin-7/2 nucleus, form a three qubit system. A general procedure is given, for implementing a controlled phase shift gate on a system consisting of any number of energy levels. Finally Collin’s version of three-qubit DJ algorithm using multi-frequency pulses, is implemented in the spin-7/2 system.

[EN] Several authors have studied the Hadamard product or entry wise product of two matrices with di erent objectives. In particular, the product of a Hadamard matrix and the transpose of its inverse has proved useful in many areas such as in the study of chemical processes. This product is called combined matrix and is denoted by C(A). The combined matrix also has various applications in the eld of linear algebra. For example, from the combined matrix an interesting relationship between the eigenvalues and the diagonal elements of a diagonal- izable matrix is obtained. Furthermore, since the sum of each row and each column of a combined matrix is exactly equal to 1, in cases where the combined matrix is nonnegative, C(A) will be a doubly stochastic matrix. The study of properties of C(A) is still under research and many results have recently been published. Herein are collected and extended results concerning the combined matrix of some classes of matrices related to positivity? For this, a long list of related works has been consulted and a summary of the most relevant results has been made before showing the new results. The interest of some open issues was also raised. The memory is structured as follows. In the rst chapter the concepts are de ned and listed. General results are proven that will be used in the rest of the memory. In the three remaining chapters, we present the problems to solve, the results we have obtained and summarize their interest as conclusions. In Chapter 2 it is determined whether the combined matrix of some clas- sic classes of matrices may or may not be doubly stochastic. The combined matrix of these classes is studied and we concluded that the positivity of the combined matrix is obtained for some G-matrices, some H-matrices and some 2x 2 matrices. It never occurs to completely positive or completely negative ma- trices; and only it is obtained that C(A) 0 when C(A) = I in the case where A is not completely negative or M-matrix. Finally, only totally non positive anti-triangular matrices of size 2x2 have its combined matrix nonnegative. In Chapter 3 the previous study is extended to sign-regular matrices. The sign of the entries of the combined matrix from the signature of the matrix and of its inverse matrix transpose is analyzed and a list with all possible cases is obtained. This list shows cases where C(A) is never negative and others where C(A) is nonnegative when it is a diagonal or anti-diagonal matrix, that is, only when C(A) coincides with the identity matrix I or the anti-identity J. Likewise, it follows that the sign of the elements in C(A) is determined solely by the rst two and the last two elements of the symbol of A. In Chapter 4, we determine relations between the diagonal elements of the combined matrix of a totally negative matrix and thereby we characterize when a given vector can be the diagonal entries of C(A). Thus, relations between the rst two and last two diagonal elements of C(A), both for symmetric and non- symmetric cases are obtained. The diagonal of a combined matrix of a totally negative matrix of dimension 3x3 is also characterized. Finally, a chapter is written with all our achievements and a short list of possible future lines of work upon aspects that the author of this report would like to continue studying in order to reach new related goals. / [ES] El producto de Hadamard o producto elemento a elemento de dos matrices ha sido estudiado por diversos autores con diferentes objetivos. En particular, el producto de Hadamard de una matriz y la traspuesta de su inversa ha de- mostrado su utilidad en múltiples áreas como por ejemplo en el estudio de procesos químicos. Este producto se denomina matriz combinada y se denota por C(A). La matriz combinada tiene además diversas aplicaciones en el ámbito del álgebra lineal. A partir de la matriz combinada se obtiene, por ejemplo, una interesante relación entre los valores propios y los elementos diagonales de una matriz diago- nalizable. Además, dado que la suma de cada fi la y de cada columna de una matriz combinada es exactamente igual a 1, en aquellos casos en que la matriz combinada sea no negativa, C(A) será una matriz doblemente estocástica. El es- tudio de propiedades de C(A) sigue siendo de actualidad y muchos resultados han sido publicados recientemente. En esta memoria se recogen y amplían los resultados referentes a la matriz combinada de algunas clases de matrices relacionadas con la positividad. Para ello se ha consultado una larga relación de trabajos relacionados y se ha realizado un resumen de los resultados más relevantes antes de incluir los nuevos resultados. Se plantea también el interés de algunas cuestiones abiertas. La memoria se estructura de la siguiente manera. En el primer capítulo se de nen los conceptos y se enuncian y/o demuestran los resultados de ámbito general que van a ser utilizados en el resto de la memoria. En los tres restantes capítulos se plantea el tipo de problema a resolver, se enuncian y demuestran los resultados obtenidos y se resume su interés a modo de conclusiones. En el Capítulo 2 se determina si la matriz combinada de clásicas clases de matrices puede ser o no doblemente estocástica. Se estudia la matriz combinada de estas clases y se concluye que se obtiene la positividad de la matriz combinada para algunas G-matrices, algunas H-matrices y algunas matrices 2x2; nunca se da para matrices totalmente positivas o totalmente negativas; y s'olo se obtiene C(A) mayor o igual que 0 cuando C(A) = I en el caso de que A sea totalmente no negativa o M-matriz. Por último, sólo las matrices anti-triangulares totalmente no positivas de tamaño 2x2 tienen matriz combinada no negativa. En el Capítulo 3 se extiende el estudio anterior a matrices signo-regulares. Se analiza el signo de las entradas de la matriz combinada a partir de la signatura de la matriz y de la signatura de su matriz inversa traspuesta y se obtiene una lista con todos los casos posibles. Esta lista muestra casos en los que C(A) nunca es no negativa y otros en los que C(A) es no negativa cuando es una matriz diagonal o anti-diagonal, esto es, sólo cuando C(A) coincide con la matriz identidad, I, o con la anti-identidad, J. Así mismo, se deduce que el signo de los elementos de C(A) viene determinado únicamente por los dos primeros y los dos últimos elementos de la signatura de A. En el Capítulo 4 se busca determinar relaciones entre los elementos diagonales de la matriz combinada de una matriz totalmente negativa y con ello caracterizar cuándo cierto vector puede coincidir con la diagonal de C(A). Así, se obtienen relaciones entre los dos primeros y dos últimos elementos de la diagonal de C(A), tanto para el caso simétrico como no simétrico. También se caracteriza la diagonal de la matriz combinada de una matriz totalmente negativa de dimensión 3x3. Finalmente, se incluye un capítulo donde se resume los logros alcanzados y un pequeño listado de las posibles líneas futuras de trabajo sobre aspectos que el autor de esta memoria querría continuar estudiando en vista a unos nuevos objetivos. / [CAT] El producte de Hadamard o producte element a element de dues matrius ha sigut estudiat per diversos autors amb diferents objectius. En particular, el pro- ducte de Hadamard d'una matriu i la trasposta de la seua inversa ha demostrat la seua utilitat en mltiples rees com per exemple en l'estudi de processos qumics. Aquest producte es denomina matriu combinada i es denota per C(A). La ma- triu combinada t a ms diverses aplicacions en l'mbit de l'lgebra lineal. A partir de la matriu combinada s'obt, per exemple, una interessant relaci entre els val- ors propis i els elements diagonals d'una matriu diagonalizable. A ms, ats que la suma de cada la i de cada columna d'una matriu combinada s exactament igual a 1, en aquells casos en qu la matriu combinada siga no negativa, C(A) ser una matriu doblement estocstica. L'estudi de propietats de C(A) segueix sent d'actualitat i molts resultats han sigut publicats recentment. En aquesta memria s'arrepleguen i amplien els resultats referents a la matriu combinada d'algunes classes de matrius relacionades amb la positividad. Per a a s'ha consultat una llarga relaci de treballs relacionats i s'ha realitzat un resum dels resultats ms rellevants abans d'incloure els nous resultats. Es planteja tamb l'inters d'algunes qestions obertes. La memria s'estructura de la segent manera. En el primer captol es de- neixen els conceptes i s'enuncien i/o demostren els resultats d'mbit general que van a ser utilitzats en la resta de la memria. En els tres restants captols es planteja el tipus de problema a resoldre, s'enuncien i demostren els resultats obtinguts i es resumeix el seu inters a manera de conclusions. En el Captol 2 es determina si la matriu combinada de clssiques classes de matrius pot ser o no doblement estocstica. S'estudia la matriu combinada d'aquestes classes i es conclou que s'obt la positividad de la matriu combinada per a algunes G-matrius, algunes H-matrius i algunes matrius 2 x2; mai es dna per a matrius totalment positives o totalment negatives; i noms s'obt C(A) 0 quan C(A) = I en el cas que A siga totalment no negativa o M-matriu. Finalment, noms les matrius anti-triangulars totalment no positives de grandria 2x2 tenen matriu combinada no negativa. En el Captol 3 s'estn l'estudi anterior a matrius signe-regulars. S'analitza el signe de les entrades de la matriu combinada a partir de la signatura de la matriu i de la signatura de la seua matriu inversa trasposta i s'obt una llista amb tots els casos possibles. Aquesta llista mostra casos en els quals C(A) mai s no negativa i uns altres en els quals C(A) s no negativa quan s una matriu diagonal o anti-diagonal, a s, noms quan C(A) coincideix amb la matriu identitat I o amb la anti-identitat J. Aix mateix, es dedueix que el signe dels elements de C(A) ve determinat nicament pels dos primers i els dos ltims elements de la signatura de A. En el Captol 4 se cerca determinar relacions entre els elements diagonals de la matriu combinada d'una matriu totalment negativa i amb a caracteritzar quan cert vector pot coincidir amb la diagonal de C(A). Aix, s'obtenen relacions entre els dos primers i dos ltims elements de la diagonal de C(A), tant per al cas simtric com no simtric. Tamb es caracteritza la diagonal de la matriu combinada d'una matriu totalment negativa de dimensi 3x3. Finalment, s'inclou un captol on es resumeix els assoliments aconseguits i un petit llistat de les possibles lnies futures de treball sobre aspectes que l'autor d'aquesta memria voldria continuar estudiant en vista a uns nous objectius. / Santana De Asís, MDJ. (2015). MATRICES COMBINADAS DE ALGUNOS TIPOS DE MATRICES [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48806 / TESIS

Cette thèse est consacrée à l'analyse mathématique de l'équation d'Euler incompressible à surface libre. On se concentre sur la propriété dispersive et sur la théorie de Cauchy à faible régularité. Une grande part de la thèse est consacrée à l'étude de l'équation des ondes de gravité-capillarité. On établit des critères d'explosion et la persistance de régularité dans les espaces de Sobolev. En démontrant les estimations de Strichartz pour les solutions à faible régularité, on obtient des théories de Cauchy pour les données initiales dont la vitesse peut être non-lipschitzienne. Dans une autre part de la thèse, on étudie la propriété dispersive des équations des ondes de surface. Plus précisément, on s'intéresse aux estimations de Strichartz. On démontre que, pour les solutions raisonnablement régulières, les équations des ondes de surface non linéaires obéissent aux mêmes estimations de Strichartz comme dans le cas des équations linéarisées. / This dissertation is devoted to the mathematical analysis of the water waves systems. We focus on the dispersive property and the Cauchy problem for rough initial data. One of the main objects of study is the gravity-capillary water waves system. We establish blow-up criteria and the persistence of Sobolev regularity. By proving Strichartz estimates for rough solutions, we obtain Cauchy theories for non-Lipschitz initial velocity. In another part of the dissertation, we study the dispersive property of the fully nonlinear water waves systems. More specifically, we are interested in Strichartz estimates. We prove for sufficiently smooth solutions that the nonlinear systems obey the same Strichartz estimates as their linearizations do.

The subject of this work deals with the problem of channel estimation for CDMA systems. This method of multiple access when individual users share the same full bandwidth simultaneously and are differentiated with any of pseudorandom sequences, is now the most perspective method. That is proved by its wide implementation in mobile networks of the third generation and higher systems. This work describes basic theory principles of spread spectrum, above all DS-CDMA (Direct Sequence-CDMA) and furthermore some phenomena of radio wireless channel that affect changes in transmitted signal in its way from transmitter to receiver. Terms of fading, multipath propagation, loss, refraction, scattering of the wave and Rice and Rayleigh probability density functions are mentioned. The third chapter deals with yet known and used capabilities of channel estimation. Differences, advantages and disadvantages of so-called blind estimation or training-based estimation are discussed. Two algorithms: LS method and sliding correlator are analyzed in more detail. There is also description of their simulations in Matlab and some results of these simulations are discussed. The last chapter deals with comparison of main characteristics and achievable accuracy of wireless channel impulse response estimation by both methods, and their possible utilization in real live.

<p>The recent groundbreaking demonstrations of quantum supremacy in noisy intermediate scale quantum (NISQ) computing era has triggered an intense activity in establishing finer boundaries between classical and quantum computing. In this dissertation, we use established techniques based on quantum Monte Carlo (QMC) to map quantum problems into probabilistic networks where the fundamental unit of computation, p-bit, is inherently probabilistic and can be tuned to fluctuate between ‘0’ and ‘1’ with desired probability. We can view this mapped network as a Boltzmann machine whose states each represent a Feynman path leading from an initial configuration of q-bits to a final configuration. Each such path, in general, has a complex amplitude, ψ which can be associated with a complex energy. The real part of this energy can be used to generate samples of Feynman paths in the usual way, while the imaginary part is accounted for by treating the samples as complex entities, unlike ordinary Boltzmann machines where samples are positive. This mapping of a quantum circuit onto a Boltzmann machine with complex energies should be particularly useful in view of the advent of special-purpose hardware accelerators known as Ising Machines which can obtain a very large number of samples per second through massively parallel operation. We also demonstrate this acceleration using a recently used quantum problem and speeding its QMC simulation by a factor of ∼ 1000× compared to a highly optimized CPU program. Although this speed-up has been demonstrated using a graph colored architecture in FPGA, we project another ∼ 100× improvement with an architecture that utilizes clockless analog circuits. We believe that this will contribute significantly to the growing efforts to push the boundaries of the simulability of quantum circuits with classical/probabilistic resources and comparing them with NISQ-era quantum computers. </p>

This thesis is devoted to the study of optimal control problems governed by a quasistatic, thermoviscoplastic model at small strains with linear kinematic hardening, von Mises yield condition and mixed boundary conditions. Mathematically, the thermoviscoplastic equations are given by nonlinear partial differential equations and a variational inequality of second kind in order to represent the elastic, plastic and thermal effects. Taking into account thermal effects we have to handle numerous mathematical challenges during the analysis of the thermoviscoplastic model, mainly due to the low integrability of the nonlinear terms on the right-hand side of the heat equation. One of our main results is the existence of a unique weak solution, which is proved by means of a fixed-point argument and by employing maximal parabolic regularity theory. Furthermore, we define the related control-to-state mapping and investigate properties of this mapping such as boundedness, weak continuity and local Lipschitz continuity. Another major result is the finding that the mapping is Hadamard differentiable; a main ingredient is the reformulation of the variational inequality, the so called viscoplastic flow rule, as a Banach space-valued ordinary differential equation with non-differentiable right-hand side. Subsequently, we consider an optimal control problem governed by thermoviscoplasticity and show the existence of a minimizer. Finally, close this thesis with numerical examples. / Diese Arbeit ist der Untersuchung von Optimalsteuerproblemen gewidmet, denen ein quasistatisches, thermoviskoplastisches Model mit kleinen Deformationen, mit linearem kinematischen Hardening, von Mises Fließbedingung und gemischten Randbedingungen zu Grunde liegt. Mathematisch werden thermoviskoplastische Systeme durch nichtlineare partielle Differentialgleichungen und eine variationelle Ungleichung der zweiten Art beschrieben, um die elastischen, plastischen und thermischen Effekte abzubilden. Durch die Miteinbeziehung thermischer Effekte, treten verschiedene mathematische Schwierigkeiten während der Analysis des thermoviskoplastischen Systems auf, die ihren Ursprung hauptsächlich in der schlechten Regularität der nichtlinearen Terme auf der rechten Seite der Wärmeleitungsgleichung haben. Eines unserer Hauptresultate ist die Existenz einer eindeutigen schwachen Lösung, welches wir mit Hilfe von einem Fixpunktargument und unter Anwendung von maximaler parabolischer Regularitätstheorie beweisen. Zudem definieren wir die entsprechende Steuerungs-Zustands-Abbildung und untersuchen Eigenschaften dieser Abbildung wie die Beschränktheit, schwache Stetigkeit und lokale Lipschitz Stetigkeit. Ein weiteres wichtiges Resultat ist, dass die Abbildung Hadamard differenzierbar ist; Hauptbestandteil des Beweises ist die Umformulierung der variationellen Ungleichung, der sogenannten viskoplastischen Fließregel, als eine Banachraum-wertige gewöhnliche Differentialgleichung mit nichtdifferenzierbarer rechter Seite. Schließlich runden wir diese Arbeit mit numerischen Beispielen ab.

Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient, ... / This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term ...

La RMN est une méthode de choix pour la détermination de la structure tridimensionnelle des protéines et des acides nucléiques en solution. Cependant, la taille des systèmes que l'on peut étudier actuellement par RMN est limitée. Dans la première partie de ce travail, la structure du répresseur BlaI de la beta-lactamase de B. licheniformis 749/I et son interaction avec l'ADN ont été étudiées par RMN avec des méthodes classiques. Ces résultats ont permis de mieux caractériser la répression des gènes de plusieurs mécanismes de résistance aux antibiotiques, incluant la résistance à la méthicilline de la souche pathogène S. aureus. Le deuxième volet de ce travail concerne l'implémentation de filtres Hadamard qui augmentent la résolution des spectres dans certaines expériences de RMN multidimensionnelle. Ces filtres permettent de séparer les pics de corrélation des protéines et des acides nucléiques selon le type d'acide aminé et le type de base, respectivement. Ces développements ouvrent de nouveaux horizons vers l'étude de macromolécules biologiques de plus grosse taille par RMN.