Let P and Q be two idempotents, we review the results about the equivalence between the invertibility of a linear combination aP +bQ and that of P +Q, where a and b are any nonzero complex numbers with a + b eq 0. It is possible to extend the results to the case P and Q are square-zero elements. However, we will show that these extensions are impossible in general for P and Q being partial isometries or n-potents with n geq 3. We will show in case P and Q are square-zero elements, the invertibility of P +Q is equivalent to that of aP +bQ for nonzero a, b.

Mapping anomalies in the Earth’s magnetic field is one method used in applied geophysics, for exploring buried structures and objects. Magnetic surveys can be ground-based or made airborne, onboard airplanes, helicopters, or unmanned aerial vehicles (UAV), also known as drones. The measurements in this project were made as part of a mapping project by the Swedish Geological Survey (SGU) in the Enåsen area in Hälsingland, central Sweden. The magnetic data were collected by SGU in the field summer of 2021. The aim of this project is to model the data from UAV-borne surveys and validate them by checking the response with the measure ground-based data collected by SGU and compare several different profiles to investigate the different results from ground-based vs. UAV-borne surveys. Two models from two different UAV flight lines were made using the software Potent, to show anomalies in the magnetic field intensity. The modelling results show a relatively good correlation between the response from the model and ground-based data. However, there are detailed variations in the ground-based data that are not resolved by the UAV data. This is partly because of the height difference and partly different sampling. The magnetic anomalies in the project area were interpreted, with the help of the modelled profiles, as being caused mainly by geological units consisting of metasedimentary rock/migmatite. These units generally dip with 30-50°, some of them containing Cuand Au-mineralizations. The dip, rock type, and magnetic susceptbilities of these units match the field data from SGU relatively well and are also backed up by SGU models of electrical resistivity from the same area. / Kartläggning av avvikelser i jordens magnetfält är en metod som används inom tillämpad geofysik för att upptäcka underjordiska strukturer och objekt. Magnetiska undersökningar kan utföras på marken eller från luften, med hjälp av flygplan, helikopter eller drönare. De geofysiska mätningarna i detta projekt gjordes som en del av ett karteringsprojekt av Sveriges geologiska undersökning (SGU) i Enåsen, Hälsingland. Dessa magnetiska data insamlades av SGU under sommaren 2021. Syftet med projektet är att modellera magnetiska data insamlade med hjälp av drönare, för att sedan kontrollera modellerna med magnetiska markdata insamlade av SGU i samma område. Dessa profiler jämfördes för att undersöka hur insamlad data från drönare respektive markmätningar skiljer sig. Modellerna gjordes i programvaran Potent, där anomalierna i magnetfältets intensitet. Resultaten från modelleringen visar en relativt tydlig korrelation mellan hur modellen (från insamlade drönardata) svarar mot markdata. Det förekommer dock små variationer i profilerna från markdata, som inte syns i modellerna från drönardata. Detta beror delvis på att mätningarna gjordes på olika höjd, och delvis på att proverna skiljer sig åt i viss mån. De magnetiska anomalierna i projektområdet tolkades med hjälp av de modellerade profilerna, och förmodas vara orsakade av enheter av metasedimentär bergart/migmatit. Dessa enheter stupar mestadels med 30-50°, och på vissa platser förekommer Cu- och Au-mineraliseringar. Stupningen, bergarter och den magnetiska susceptibiliteten stämmer relativt väl överens med SGU:s information från fältundersökningar, och tolkningen styrks ytterligare av SGU:s modeller av den elektriska resistiviteten i samma område.

Coronary artery disease and chronic pain are serious health issues that cause severe discomfort and suffering in society today. Antithrombotic agents and highly potent analgesics play a critical role in improving the recovery process for patients being treated for these diseases. This thesis focuses on the design and study of pellet-based drug dosage forms which allow diffusion-controlled delivery of drugs with the aim of achieving optimal therapeutic outcomes. A wet slurry process was used to mix the drug and the polymer and/or clay precursor excipients into a paste. The pellets were then shaped via ionotropic gelation (alginate hydrogel beads/pellets), extrusion/spheronization (halloysite clay pellets) or geopolymerization. The decrease in the drug diffusion rate in the alginate beads was affected by the drug's molecular size and charge and the characteristics (such as concentration and chemical structure) of the surrounding alginate gel. The halloysite clay pellets provided sustained release of the highly potent drug fentanyl at both gastric pH 1 and intestinal pH 6.8. As expected, crushing the pellets reduced the diffusion barrier, resulting in more rapid release (dose dumping). The use of mechanically strong geopolymer gels was investigated as a potential means of preventing dose dumping as a result of crushing of the dosage form. Variations in the synthesis composition resulted in drastic changes in the microstructure morphology, the porosity, the mechanical stability and the drug release rate. Pore network modeling and finite element simulations were employed to theoretically evaluate the effects of porosity and drug solubility in the geopolymer structure on the drug release process. Fitting the model parameters to experimental data showed that increased average pore connectivity, a greater pore size distribution, and increased drug solubility in the pellet resulted in an increased drug release rate. Furthermore, incorporation of pH-sensitive organic polymers in the geopolymer structure reduced the high drug release rate from the pellets at gastric pH. These results indicate that geopolymers have potential for use in pellet form; both the release rate of the drug and the mechanical stability of the pellets can be optimized to prevent dose dumping.

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = Xr1 + Xr2 + ... + Xrt and r1>r2>...>rt≥2. In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We also extended these results to linear operators that strongly preserve the matrix polynomial equation p(X) = I where p(X) is as above. Chapters I and II of this thesis contain background material and summaries of the work done by other researchers on the linear preserver problem. Characterizations of linear operators in chapters III, IV, V, and VI of this thesis are new.

Esta investigação teórica procura identificar pontos de aproximação entre o conceito de potência orgástica, formulado pelo psiquiatra e psicanalista austríaco Wilhelm Reich (1897-1957), e o desempenho esportivo. Para isso procuramos focalizar o processo de evolução do conceito tendo como base os textos em que o apresenta e o define, partindo então para a exploração a respeito do conjunto de matizes e nuances que constituem a visão particular que Reich atribui ao termo potência. Em seguida, buscamos realizar essa aproximação com o desempenho esportivo nos sustentando em pesquisadores do tema, de modo a estabelecer pontos comuns de diálogo e similitudes que permitem um olhar sobre o desempenho esportivo à luz da obra reichiana, com especial ênfase à sua visão de potência. Por fim, fazemos uso da contribuição original de Albertini (1997) a respeito dos encontros potentes como forma de adicionar elementos à nossa reflexão e oferecer contribuições à compreensão do desempenho esportivo sob a ótica da psicologia profunda. Entendido primeiramente como a capacidade do indivíduo de se entregar ao fluxo de suas excitações sexuais no ato amoroso, de modo a atingir o orgasmo e assim descarregar sua libido represada, a evolução da obra de Reich aponta para a utilização do conceito de potência em outras dimensões da vida, nos levando a compreender que a visão de potência em Reich se refere à capacidade de ser humano estar presente e entregar-se em tudo aquilo que realiza. Essa visão se aproxima de conceitos utilizados na psicologia do esporte a respeito de estados ótimos de prontidão para o desempenho esportivo, apontados por alguns autores como ideais para a obtenção de resultados superiores. Essa aproximação, quando colocada sob o prisma da ideia de encontros potentes, nos permite reavaliar os aspectos estruturais que o conceito de potência possui no pensamento reichiano, assim como considerar a interferência dos processos transferenciais no desempenho esportivo, apontando para a ideia de que o desempenho esportivo não é afetado apenas por condições psíquicas individuais e isoladas do meio, mas especialmente pelo campo transferencial que se compõe no momento em que o desempenho ocorre / This theoretical investigation aim at the identification of approach points between the concept of orgastic potency, formulated by the Austrian psychiatrist and psychoanalyst Wilhelm Reich (1897-1957), and sport performance. To achieve this intent we first try to focus on the concept´s development process, based on the writings in which Reich presents it and defines it. Then, we continue to search and exploit the set of shades and nuances that make up the particular vision that Reich gives to the term potency. Following, we seek to achieve this approach to sports performance with the support of researchers in this area, in order to establish a common ground of dialogue and point out similarities that allow a glimpse into sports performance through the light of Reich\'s work, with special emphasis on his vision of potency. Finally, we use the original contribution of Albertini (1997) about the \"potent encounters\" as a way to add elements to our reflection and offer contributions to the understanding of sports performance from the perspective of depth psychology. Understood primarily as the ability of an individual to surrender to the free flow of his sexual excitations in lovemaking, in order to achieve orgasm and so discharge their repressed libido, the evolution of this concept points to the use of the term potency in other dimensions of life. Thus, leading us to the understanding that potency, in Reich´s view, refers to the ability of human beings to surrender and be present in everything they do in life. This view is similar to some sport psychology´s concepts about optimal states and readiness for performance, pointed out by some authors as ideal for achieving superior results. This approach, when placed under the light of the potent encounter´s notion, allows us to re-evaluate the structural aspects that the potency concept has on Reich\'s thinking, as well as to consider the interference of transference processes in sports performance. With this we were able to point at the idea that sport performance are not influenced only by individual and isolated psychological conditions, but specially by the transference field composed at/in the moment the performance occurs

Esta investigação teórica procura identificar pontos de aproximação entre o conceito de potência orgástica, formulado pelo psiquiatra e psicanalista austríaco Wilhelm Reich (1897-1957), e o desempenho esportivo. Para isso procuramos focalizar o processo de evolução do conceito tendo como base os textos em que o apresenta e o define, partindo então para a exploração a respeito do conjunto de matizes e nuances que constituem a visão particular que Reich atribui ao termo potência. Em seguida, buscamos realizar essa aproximação com o desempenho esportivo nos sustentando em pesquisadores do tema, de modo a estabelecer pontos comuns de diálogo e similitudes que permitem um olhar sobre o desempenho esportivo à luz da obra reichiana, com especial ênfase à sua visão de potência. Por fim, fazemos uso da contribuição original de Albertini (1997) a respeito dos encontros potentes como forma de adicionar elementos à nossa reflexão e oferecer contribuições à compreensão do desempenho esportivo sob a ótica da psicologia profunda. Entendido primeiramente como a capacidade do indivíduo de se entregar ao fluxo de suas excitações sexuais no ato amoroso, de modo a atingir o orgasmo e assim descarregar sua libido represada, a evolução da obra de Reich aponta para a utilização do conceito de potência em outras dimensões da vida, nos levando a compreender que a visão de potência em Reich se refere à capacidade de ser humano estar presente e entregar-se em tudo aquilo que realiza. Essa visão se aproxima de conceitos utilizados na psicologia do esporte a respeito de estados ótimos de prontidão para o desempenho esportivo, apontados por alguns autores como ideais para a obtenção de resultados superiores. Essa aproximação, quando colocada sob o prisma da ideia de encontros potentes, nos permite reavaliar os aspectos estruturais que o conceito de potência possui no pensamento reichiano, assim como considerar a interferência dos processos transferenciais no desempenho esportivo, apontando para a ideia de que o desempenho esportivo não é afetado apenas por condições psíquicas individuais e isoladas do meio, mas especialmente pelo campo transferencial que se compõe no momento em que o desempenho ocorre / This theoretical investigation aim at the identification of approach points between the concept of orgastic potency, formulated by the Austrian psychiatrist and psychoanalyst Wilhelm Reich (1897-1957), and sport performance. To achieve this intent we first try to focus on the concept´s development process, based on the writings in which Reich presents it and defines it. Then, we continue to search and exploit the set of shades and nuances that make up the particular vision that Reich gives to the term potency. Following, we seek to achieve this approach to sports performance with the support of researchers in this area, in order to establish a common ground of dialogue and point out similarities that allow a glimpse into sports performance through the light of Reich\'s work, with special emphasis on his vision of potency. Finally, we use the original contribution of Albertini (1997) about the \"potent encounters\" as a way to add elements to our reflection and offer contributions to the understanding of sports performance from the perspective of depth psychology. Understood primarily as the ability of an individual to surrender to the free flow of his sexual excitations in lovemaking, in order to achieve orgasm and so discharge their repressed libido, the evolution of this concept points to the use of the term potency in other dimensions of life. Thus, leading us to the understanding that potency, in Reich´s view, refers to the ability of human beings to surrender and be present in everything they do in life. This view is similar to some sport psychology´s concepts about optimal states and readiness for performance, pointed out by some authors as ideal for achieving superior results. This approach, when placed under the light of the potent encounter´s notion, allows us to re-evaluate the structural aspects that the potency concept has on Reich\'s thinking, as well as to consider the interference of transference processes in sports performance. With this we were able to point at the idea that sport performance are not influenced only by individual and isolated psychological conditions, but specially by the transference field composed at/in the moment the performance occurs

In heterogeneous dense networks where spectrum is shared, users' privacy remains one of the major challenges. On a multi-antenna relay-assisted multi-carrier interference channel, each user shares the spectral and spatial resources with all other users. When the receivers are not only interested in their own signals but also in eavesdropping other users' signals, the cross talk on the spectral and spatial channels becomes information leakage. In this paper, we propose a novel secrecy rate enhancing relay strategy that utilizes both spectral and spatial resources, termed as information leakage neutralization. To this end, the relay matrix is chosen such that the effective channel from the transmitter to the colluding eavesdropper is equal to the negative of the effective channel over the relay to the colluding eavesdropper and thus the information leakage to zero. Interestingly, the optimal relay matrix in general is not block-diagonal which encourages users' encoding over the frequency channels. We proposed two information leakage neutralization strategies, namely efficient information leakage neutralization (EFFIN) and local-optimized information leakage neutralization (LOPTIN). EFFIN provides a simple and efficient design of relay processing matrix and precoding matrices at the transmitters in the scenario of limited power and computational resources. LOPTIN, despite its higher complexity, provides a better sum secrecy rate performance by optimizing the relay processing matrix and the precoding matrices jointly. The proposed methods are shown to improve the sum secrecy rates over several state-of-the-art baseline methods.

In heterogeneous dense networks where spectrum is shared, users' privacy remains one of the major challenges. On a multi-antenna relay-assisted multi-carrier interference channel, each user shares the spectral and spatial resources with all other users. When the receivers are not only interested in their own signals but also in eavesdropping other users' signals, the cross talk on the spectral and spatial channels becomes information leakage. In this paper, we propose a novel secrecy rate enhancing relay strategy that utilizes both spectral and spatial resources, termed as information leakage neutralization. To this end, the relay matrix is chosen such that the effective channel from the transmitter to the colluding eavesdropper is equal to the negative of the effective channel over the relay to the colluding eavesdropper and thus the information leakage to zero. Interestingly, the optimal relay matrix in general is not block-diagonal which encourages users' encoding over the frequency channels. We proposed two information leakage neutralization strategies, namely efficient information leakage neutralization (EFFIN) and local-optimized information leakage neutralization (LOPTIN). EFFIN provides a simple and efficient design of relay processing matrix and precoding matrices at the transmitters in the scenario of limited power and computational resources. LOPTIN, despite its higher complexity, provides a better sum secrecy rate performance by optimizing the relay processing matrix and the precoding matrices jointly. The proposed methods are shown to improve the sum secrecy rates over several state-of-the-art baseline methods.