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In this article, a continuous-time complex-valued projection neural network (CCPNN) in a matrix state space is first proposed for a general complex-variable basis pursuit problem. The proposed CCPNN is proved to be stable in the sense of Lyapunov and to be globally convergent to the optimal solution under the condition that the sensing matrix is not row full rank. Furthermore, an improved discrete-time complex projection neural network (IDCPNN) is proposed by discretizing the CCPNN model. The proposed IDCPNN consists of a two-step stop strategy to reduce the calculational cost. The proposed IDCPNN is theoretically guaranteed to be global convergent to the optimal solution. Finally, the proposed IDCPNN is applied to the reconstruction of sparse signals based on compressed sensing. Computed results show that the proposed IDCPNN is superior to related complex-valued neural networks and conventional basis pursuit algorithms in terms of solution quality and computation time.

We develop a matrix form of the Nelder-Mead simplex method and show that its convergence is related to the convergence of infinite matrix products. We then characterize the spectra of the involved matrices necessary for the study of convergence. Using these results, we discuss several examples of possible convergence or failure modes. Then, we prove a general convergence theorem for the simplex sequences generated by the method. The key assumption of the convergence theorem is proved in low-dimensional spaces up to 8 dimensions.

В статье рассматриваются различные формы записи комплексных и гиперкомплексных чисел: алгебраическая (стандартная); в парах; матричная форма. Приведены примеры вычислений в перечисленных способах записи чисел.

The collection of information on non-payments in the banking sector and their compact presentation in the matrix form in accordance with the required rules, the creation of various economic models (equities) of non-payments, elimination of different non-payment consequences and analysis are the intermediate scientific research goal of the article.

This article deals with the generalization of the matrix form of the Oresme sequence, extending it to the field of integers. In addition, the two valid generating matrices were discussed, through the permutation of the rows and columns, respectively, totaling two valid matrices of Oresme for the left-hand side, and two more generating matrices of Oresme for the right-hand side. In addition, a new Oresme sequence was introduced, given through the hybridization process of these numbers, obtaining mathematical properties and theorems, inherent to this process.

The matrix form of the reciprocity relationship for the ABCD matrix of a general distributed microwave circuit featuring multiple ports is revisited. The correct reciprocity relationship is used to identify mistakes previously made in the derivation of key relations in the vector-short-open-calibration (VSOC) deembedding methodology, which is commonly used for removing the effect of port discontinuities in the Method-of-Moments-based electronic design automation (EDA) models of microwave circuits, digital interconnects, and other structures. Numerical results demonstrating the impact of the incorrect reciprocity relation on the accuracy of VSOC deembedding are provided.

Začetnik Bečke oftalmološke škole bio je prof. dr. Georg Joseph Beer koji je 1812. u Beču u Općoj bolnici osnovao Prvu sveučilišnu očnu kliniku u svijetu. Prof. Ferdinand von Arlt vodio ju je 27 godina, od 1856. do 1883. Budući da je prva očna klinika postala pretijesna, u istoj je bolnici u Beču 1883. osnovana Druga sveučilišna očna klinika. Od 1885. trideset ju je godina vodio prof. Ernst Fuchs. Mnogi su poznati oftalmolozi još vodili te dvije bečke očne klinike, ali Arlt i Fuchs su bili glavni predstavnici Bečke oftalmološke škole koja se uvijek odlikovala visokim mjerilima u dijagnostici i liječenju očnih bolesti. Mnogi hrvatski oftalmolozi educirali su se kod njih ili kod njihovih učenika te osnivali očne odjele u većim gradovima u Hrvatskoj prenoseći stečeno znanje i iskustvo. Prvi očni odjeli u Hrvatskoj osnovani su na prijelazu iz 19. u 20. stoljeće. Prva sveučilišna očna klinika u Hrvatskoj započela je s radom u Zagrebu 1923. Naši oftalmolozi prenijeli su organizaciju klinika kakve su postojale u Beču, i to je bio tadašnji obrazac svih europskih klinika. Tradiciju Bečke oftalmološke škole prenosili su dalje, sljedećim generacijama. U radu su dane i kratke biografije bečkih i hrvatskih oftalmologa i njihovi međusobni odnosi u edukaciji i radu., The founder of the Vienna School of Ophthalmology was Prof. Dr. Georg Joseph Beer, who founded the First University Eye Clinic in the Vienna General Hospital in 1812. Prof. Ferdinand von Arlt led it for 27 years from 1856 to 1883. As the First Eye Clinic became too small, the Second University Eye Clinic was founded in 1883 at the same hospital in Vienna. Since 1885 it had been led for 30 years by Prof. Ernst Fuchs. Many well-known ophthalmologists were leading those Viennese eye clinics. However, Arlt and Fuchs were the main representatives of the Vienna School of Ophthalmology, which was always characterised by the high standards in the diagnosis and therapy of eye diseases. Many Croatian ophthalmologists were educated by them or their students, and later they established eye departments in the major cities in Croatia and transmitted acquired knowledge and experience. The first eye departments in Croatia were formed at the turn of the 19th and 20th century. The First University Eye Clinic in Croatia started to work in Zagreb in 1923. Our ophthalmologists transmitted the organisation of the clinics as they existed in Vienna, and that was the matrix form of all European clinics at that time. Therefore, the tradition of the Vienna School of Ophthalmology was passed on to the next generations. The paper also gives short biographies of Viennese and Croatian ophthalmologists and their mutual relations in education and work.

The problem of determining the body attitude in matrix form using the least-squares method is considered. A loss function that allows us to theoretically analyze the influence of the measurement errors on the accuracy of the attitude for an arbitrary number of vectors without the need for the mutual perpendicularity of the vectors. The proposed method allows us to use measurable quantities with weight coefficients.

In this study we have examined, involute of the cubic Bezier curve based on the control points with matrix form in E3. Frenet vector fields and also curvatures of involute of the cubic Bezier curve are examined based on the Frenet apparatus of the first cubic Bezier curve in E3. Â

The vertical lift gates are exposed to hydrodynamic forces that arise as a result of pressurized flow established by the large-scale effect of the water levels in the dam reservoirs. The most influential forces are those that are applied on the gate vertically upward due to the intensity of the flow under the gate and downward as a result of passage flow above the gate. The difference between these two forces generates a downpull force that is the most important gate stability indicator. In this research, an arbitrary hydraulic model was constructed to investigate the effects of many gate lip shapes with and without extensions on the magnitudes and distribution of bottom pressure coefficient when the values of flow and shaft gap width ratio (b2/bl) are constant. The results indicate that the bottom pressure coefficient appears to vary uniformly with gate openings and seem to be influenced effectively by the gate lip geometry. So, for the given value of (b2/bl), the top pressure coefficient regarding the downward force will mostly be with uniform changes and hence the downpull coefficient depends on the magnitudes and distribution of bottom pressure coefficient. An attempt by using the correlation coefficient of Statistical Package of Social Sciences was made to determine whether the pressure fluctuation is significantly shown at the bottom pressure distribution curve, which in turn is considered as appropriate indicator for the vibration occurrence. Full range of maximum bottom pressure coefficients in a matrix form is made to assist in design purposes. The results are analyzed and many conclusions are obtained.

Existing Dictionary Learning and Sparse Coding (DLSC) algorithms for Symmetric Positive Definite (SPD) matrices usually adopt Reproducing Kernel Hilbert Space as workspace to perform necessary linear operations. But those methods heavily rely on ideal kernel maps and they are lack of robustness when facing different SPD data, especially in the case of high-sparsity coding. Different from existing methods, we explore a new workspace called Symmetric Matrices Inner Product Space (SMIPS) for modeling robust DLSC of SPD matrices. SMIPS, which can be treated as the minimal linear expansion space of SPD manifold, is a linear space equipped with a pre-defined inner product so it supports linear operations. Modelling DLSC in SMIPS is more intuitive, and SPD data can preserve matrix form in SMIPS. Then, in this paper, a Riemannian Geometry Preserving (RGP) method based on graph-regularized is proposed to include the Riemannian geometric information of original SPD data, so that improves the discriminability of sparse codes, and a sparse coding algorithm is developed to acquire sparse codes of SPD matrices in SMIPS efficiently, which extend the feature-sign search to such matrix space. For dictionary learning, an overall learning strategy utilizing the closed form solution of RGP codes is proposed to speed up the iterative dictionary learning process. Experiments on several computer vision tasks show that our algorithm is more robust even with high-sparsity coding across different datasets and outperforms other comparative algorithms in terms of recognition accuracy and learning efficiency, which also demonstrates the validity of SMIPS as a workspace.

The mathematical modelling of the dynamics of a helicopter underslung system consisting of multiple rigid bodies interconnected by cables is described in this paper. The differential equations of motion are derived using the matrix form of Kane’s method. This avoids the enormous complexity involved in symbolic derivations, which are usually available in the published literature. The generalized coordinates and generalized speeds are selected suitably to derive the kinematical relationships describing the motion of the joints and centres of gravity of the different bodies present in the underslung system. The formulated model is validated using the principle of conservation of mechanical energy neglecting the dissipative forces. Simulation results demonstrating the characteristic motion of the system are presented.

In recent years, the airport’s influence on economic development has become stronger. Airport economy has become the new engine of promoting regional economic development. As a resource-based city, Dalian has included the development of airport economy in Dalian’s Development Plan, focusing on building airport economy circle, to make airport economy as an important section of driving regional economic development. SWOT stands for: strengths, weaknesses, opportunities, threats. The so-called SWOT analysis is based on the internal and external competitive environment and competitive conditions of the situation. The main internal advantages, disadvantages and external opportunities and threats that are closely related to the research object are listed through investigation, arranged according to the matrix form, and then analyzed with the idea of systematic analysis, from which a series of corresponding conclusions are drawn. In this context, this article analyzed the strengths, weaknesses, opportunities and threats of developing airport economy in Dalian, and proposed the strategic choice of the development of airport economy in Dalian.

This paper describes the development and testing of a lab plant that emulates a water supply pumping system with the objective of testing optimal pumping strategies based on standard solvers. The emulated system consists of two tanks that supply the water to two districts in a town. There are two pumps, that can fill the tanks through a reconfigurable hydraulic system with several valves. The automatic controller determines the valves and pumps that are active at each instant of time in order to minimize the operation cost, taking into account the electric tariff periods. Some aspects on the development of the lab plant are first discussed, including hydraulic aspects and real time control implementation issues. Then, a mathematical model is proposed to be able to formulate, in matrix form, the cost index and the constraints, such that, standard solvers as Mosek or CBC can be used. The full optimization proposal is tested on several experiments, and compared to some simulations, to demonstrate the validity of the plant and the optimization approach.

Дулеба Н.В. МЕТОДИЧНІ ОСНОВИ ВИЗНАЧЕННЯ РІВНЯ ЕКОНОМІЧНОЇ БЕЗПЕКИ АВТОТРАНСПОРТНОГО ПІДПРИЄМСТВА Мета. Поглиблення теоретичних основ і розробка методичних рекомендацій щодо визначення рівня економічної безпеки автотранспортного підприємства та попередження загроз втрати ним економічної безпеки. Методика дослідження. Методологічною основою статті є загальні положення економічної теорії, праці вчених економістів з питань економічної ефективності виробництва і економічної безпеки підприємств. Для аналізу стану та основних тенденцій економічної безпеки підприємства використано: метод кореляційно-регресійного аналізу - для визначення невідомих параметрів у матричному вигляді та вектора невідомих параметрів; методи економіко-математичного моделювання - для розрахунку невідомих параметрів багатофакторної регресії. Результати дослідження. Розроблено методичні основи визначення рівня економічної безпеки автотранспортного підприємства, що складаються з трьох блоків: оцінка поточного стану господарської діяльності, вибір факторів впливу на економічну безпеку та визначення рівня економічної безпеки автотранспортного підприємства, кожен з яких містить набір дій, виконання яких забезпечує перехід до наступного блоку. Наукова новизна результатів дослідження. Обґрунтовано теоретичні положення та розроблено блок-схему визначення рівня економічної безпеки автотранспортного підприємства, що базується на порівнянні чистих операційних доходів та операційних витрат автотранспортного підприємства. При перевищенні чистих операційних доходів над сукупними операційними витратами господарська діяльність автотранспортного підприємства стає прибутковою. Але для того, щоб говорити про економічну безпеку його операційної діяльності, підприємству потрібен певний рівень доходу, який буде забезпечувати покриття непередбачуваних витрат, пов’язаних із впливом внутрішніх та зовнішніх факторів – «запас міцності». Практична значущість результатів дослідження. Одержані результати дозволяють визначити рівень економічної безпеки автотранспортних підприємств та слугують підґрунтям для подальших досліджень впливу внутрішніх та зовнішніх факторів на їхню діяльність та механізму забезпечення успіху цих підприємств у довгостроковій перспективі. Ключові слова: економічна безпека, автотранспортне підприємство, запас міцності, рівні економічної безпеки, перехідна зона, вектор невідомих параметрів. Дулеба Н.В. МЕТОДИЧЕСКИЕ ОСНОВЫ ОПРЕДЕЛЕНИЯ УРОВНЯ ЭКОНОМИЧЕСКОЙ БЕЗОПАСНОСТИ АВТОТРАНСПОРТНОГО ПРЕДПРИЯТИЯ Цель. Углубление теоретических основ и разработка методических рекомендаций по определению уровня экономической безопасности автотранспортного предприятия и предупреждения угроз потери им экономической безопасности. Методика исследования. Методологической основой статьи есть общие положения экономической теории, труды ученых экономистов по вопросам экономической эффективности производства и экономической безопасности предприятий. Для анализа состояния и основных тенденций экономической безопасности предприятия использованы: метод корреляционно-регрессионного анализа - для определения неизвестных параметров в матричном виде и вектора неизвестных параметров; методы экономико-математического моделирования - для расчета неизвестных параметров многофакторной регрессии. Результаты исследования. Разработаны методические основы определения уровня экономической безопасности автотранспортного предприятия, которые состоят из трех блоков: оценка текущего состояния хозяйственной деятельности, выбор факторов влияния на экономическую безопасность и определение уровня экономической безопасности автотранспортного предприятия, каждый из которых содержит набор действий, выполнение которых обеспечивает переход к следующему блоку. Научная новизна результатов исследования. Обоснованы теоретические положения и разработана блок-схема определения уровня экономической безопасности автотранспортного предприятия, которое базируется на сравнении чистых операционных доходов и операционных расходов автотранспортного предприятия. При превышении чистых операционных доходов над совокупными операционными затратами хозяйственная деятельность автотранспортного предприятия становится прибыльной. Но для того, чтобы говорить об экономической безопасности его операционной деятельности, предприятию нужен определенный уровень дохода, который будет обеспечивать покрытие непредвиденных расходов, связанных с влиянием внутренних и внешних факторов - «запас прочности». Практическая значимость результатов исследования. Полученные результаты позволяют определить уровень экономической безопасности автотранспортных предприятий и служат основой для дальнейших исследований влияния внутренних и внешних факторов на их деятельность и механизма обеспечения успеха этих предприятий в долгосрочной перспективе. Ключевые слова: экономическая безопасность, автотранспортное предприятие, запас прочности, уровень экономической безопасности, переходная зона, вектор неизвестных параметров. Duleba N.V. METHODICAL BASES OF DEFINITION OF LEVEL OF ECONOMIC SAFETY OF THE MOTOR TRANSPORT ENTERPRISE Purpose. The aim of the article is deepening of theoretical bases and development of methodical recommendations on definition of level of economic safety of the motor transport enterprise and the prevention of threats of loss of economic safety by it. Methodology of research. The methodological basis of the article is the general provisions of economic theory, the work of economists on economic efficiency of production and economic security of enterprises. The following methods are used to analyse the state and main trends of economic security of the enterprise: the method of correlation and regression analysis - to determine the unknown parameters in matrix form and the vector of unknown parameters; methods of economic and mathematical modelling - for calculation of unknown parameters of multifactor regression. Findings. Methodical bases of definition of level of economic safety of the motor transport enterprise consisting of three blocks are developed: an estimation of a current condition of economic activity, a choice of factors of influence on economic safety and determining the level of economic security of the transport enterprise, each of which contains a set of actions, the implementation of which ensures the transition to the next block. Originality. Theoretical provisions are substantiated and the block diagram of definition of level of economic safety of the motor transport enterprise which is based on comparison of net operating incomes and operating expenses of the motor transport enterprise is developed. When the net operating income exceeds the total operating costs, the economic activity of the trucking company becomes profitable. But in order to talk about the economic security of its operating activities, the company needs a certain level of income that will cover the unforeseen costs associated with the influence of internal and external factors – “safety margin”. Practical value. The obtained results allow determining the level of economic security of motor transport enterprises and serving as a basis for further studies of the impact of internal and external factors on their activities and the mechanism for ensuring the success of these enterprises in the long term. Key words: economic security, motor transport enterprise, safety margin, levels of economic security, transition zone, vector of unknown parameters.

Die vorliegende Masterarbeit beschäftigt sich mit der Anwendbarkeit der Spieltheorie als Analysetechnik auf politische Entscheidungsprozesse. Die österreichische Innenpolitik wurde in den vergangenen Jahren immer häufiger von handfesten Skandalen erschüttert. Insbesondere in den Amtszeiten der Bundesregierungen Kurz I und Kurz II häuften sich diese. Diese Masterarbeit widmet sich genau diesem Forschungszeitraum, der österreichischen Innenpolitik zwischen Dezember 2017 bis Oktober 2021. Zunächst wird geprüft, inwiefern die Spieltheorie als Analysetechnik für die Anwendbarkeit auf politische Sachverhalte tauglich ist und im Anschluss werden zwei Regierungskrisen aus dem oben angeführten Forschungszeitraum auf spieltheoretische Elemente hin überprüft. Zum Abschluss der Arbeit werden die definierten Regierungskrisen in Spielform rekonstruiert. Das Ziel der vorliegenden Masterarbeit bewegt sich auf zwei unterschiedlichen Ebenen. Zum einen sollen politische Parteien die Entscheidungen ihrer MitbewerberInnen besser antizipieren und darauf aufbauend ihre jeweiligen Entscheidungen zielgerichteter treffen können und zum anderen sollen politische Entscheidungsprozesse für die interessierte Bevölkerung verständlicher und transparenter gemacht werden. Der theoretische Teil zu Beginn widmet sich einer allgemeinen Übersicht über die Spieltheorie. Es folgen wesentliche Begriffsdefinitionen sowie die Vorstellung einzelner spieltheoretischer Modelle. Das besondere Augenmerk liegt dabei auf jenem Bereich der Spieltheorie, der auch für politische Sachverhalte anwendbar ist. Praxisnah – mit vielen Beispielen – versucht man der interessierten Leserschaft einen verständlichen Einblick in die komplexe Materie der Spieltheorie zu vermitteln. Nach der Abhandlung der theoretischen Grundlagen folgt der Einstieg in den empirischen Teil der Arbeit. Auf Basis unterschiedlichster Daten, die in intensiver Arbeit erhoben und ausgewertet wurden, entstehen chronologische Abläufe der beiden zu begutachtenden Regierungskrisen. Diese chronologischen Sachverhaltsdarstellungen überprüft man anschließend auf das Vorliegen von spieltheoretischen Elementen. Daraus ergeben sich spannende Einblicke in das Handeln der involvierten Parteien während der Krisensituationen. Schlussendlich – aufbauend auf die Vorarbeiten aus dem Theorieteil und den Erhebungen im empirischen Teil – erfolgt eine Rekonstruktion der beiden Regierungskrisen in Spielform. Auf Basis der bereits angeführten Zielsetzung, des kurz erläuterten Einblicks in die Theorie sowie der Verwendung unterschiedlicher spieltheoretischer Elemente und Modelle, werden die eine forschungsleitende und zwei weitere Forschungsfragen beantwortet. Im Kern geht es darum, welche spieltheoretische Elemente sich während der Analyse der beiden ausgewählten Regierungskrisen finden lassen und welche Erkenntnisse man daraus ableiten kann. Die Arbeit schließt mit einem Resümee, im Zuge dessen die Erkenntnisse nochmals dargestellt und weitere Forschungsmöglichkeiten aufgezeigt werden. Aus dieser Masterarbeit ergeben sich neben hilfreichen Tipps für die politische Praxis, eben auch weitere Forschungsoptionen für Studierende, die sich sowohl für Politik als auch für strategisches Handeln interessieren. Im Anhang befindet sich ein gesondertes Inhaltsverzeichnis, in welchem klar ersichtlich wird, welcher der beiden Verfasser sich für den jeweiligen Themenbereich hauptverantwortlich zeichnet. Anzumerken ist, dass diese Arbeit im Zuge einer intensiven Zusammenarbeit entstanden ist. This master thesis deals with the applicability of game theory as an analytical technique to political decision-making processes. In recent years, Austria's domestic politics have been shaken more and more frequently by tangible scandals. Especially during the terms of office of the federal governments Kurz I and Kurz II these scandals became more frequent. The following master's thesis, will focus on exactly this research period, the Austrian domestic politics between December 2017 and October 2021. First, it will be examined to what extent game theory is suitable as an analytical technique for the applicability to political facts and subsequently, two government crises from the above research period will be examined for game-theoretical elements. Finally, the defined government crises are reconstructed in game form. The aim of this master thesis is on two different levels. On the one hand, political parties should be able to better anticipate the decisions of their competitors and, based on this, make their respective decisions more target-oriented. On the other hand, political decision-making processes should be made more understandable and transparent for the interested population. The theoretical part at the beginning is devoted to a general overview of game theory. This is followed by essential definitions of terms and the presentation of individual game theory models. Special attention is paid to those areas of game theory that are also applicable to political issues. Practical examples are given in an attempt to provide interested readers with a comprehensible insight into the complex subject of game theory. After the treatment of the theoretical bases the entrance follows into the empirical part of the work. Based on different data, which were collected and evaluated in intensive work, chronological sequences of the two government crises under review are created. These chronological factual representations are then examined for the presence of game-theoretical elements. This results in exciting insights into the actions of the parties involved during the crisis situations. Finally, building on the preliminary work from the theoretical part and the surveys in the empirical part, the two government crises are reconstructed in game form. Based on aforementioned objectives, the briefly explained insight into the theory, and the use of various game-theoretical elements and models, the one research question and two further research questions are answered. In essence, it is about which game-theoretical elements can be found during the analysis of the two selected government crises and which insights can be derived from them. The thesis concludes with a résumé, in the course of which the findings are presented again and further research possibilities are pointed out. This master thesis provides helpful tips for political practice as well as further research options for students who are interested in politics and strategic action. In the appendix there is a separate table of contents, which clearly shows which of the two authors is mainly responsible for the respective topic. It should be noted that this work was developed in the course of an intensive collaboration. Abweichender Titel laut Übersetzung der Verfasserin/des Verfassers Masterarbeit Wien, FH Campus Wien 2022

Die vorliegende Masterarbeit beschäftigt sich mit der Anwendbarkeit der Spieltheorie als Analysetechnik auf politische Entscheidungsprozesse. Die österreichische Innenpolitik wurde in den vergangenen Jahren immer häufiger von handfesten Skandalen erschüttert. Insbesondere in den Amtszeiten der Bundesregierungen Kurz I und Kurz II häuften sich diese. Diese Masterarbeit widmet sich genau diesem Forschungszeitraum, der österreichischen Innenpolitik zwischen Dezember 2017 bis Oktober 2021. Zunächst wird geprüft, inwiefern die Spieltheorie als Analysetechnik für die Anwendbarkeit auf politische Sachverhalte tauglich ist und im Anschluss werden zwei Regierungskrisen aus dem oben angeführten Forschungszeitraum auf spieltheoretische Elemente hin überprüft. Zum Abschluss der Arbeit werden die definierten Regierungskrisen in Spielform rekonstruiert. Das Ziel der vorliegenden Masterarbeit bewegt sich auf zwei unterschiedlichen Ebenen. Zum einen sollen politische Parteien die Entscheidungen ihrer MitbewerberInnen besser antizipieren und darauf aufbauend ihre jeweiligen Entscheidungen zielgerichteter treffen können und zum anderen sollen politische Entscheidungsprozesse für die interessierte Bevölkerung verständlicher und transparenter gemacht werden. Der theoretische Teil zu Beginn widmet sich einer allgemeinen Übersicht über die Spieltheorie. Es folgen wesentliche Begriffsdefinitionen sowie die Vorstellung einzelner spieltheoretischer Modelle. Das besondere Augenmerk liegt dabei auf jenem Bereich der Spieltheorie, der auch für politische Sachverhalte anwendbar ist. Praxisnah – mit vielen Beispielen – versucht man der interessierten Leserschaft einen verständlichen Einblick in die komplexe Materie der Spieltheorie zu vermitteln. Nach der Abhandlung der theoretischen Grundlagen folgt der Einstieg in den empirischen Teil der Arbeit. Auf Basis unterschiedlichster Daten, die in intensiver Arbeit erhoben und ausgewertet wurden, entstehen chronologische Abläufe der beiden zu begutachtenden Regierungskrisen. Diese chronologischen Sachverhaltsdarstellungen überprüft man anschließend auf das Vorliegen von spieltheoretischen Elementen. Daraus ergeben sich spannende Einblicke in das Handeln der involvierten Parteien während der Krisensituationen. Schlussendlich – aufbauend auf die Vorarbeiten aus dem Theorieteil und den Erhebungen im empirischen Teil – erfolgt eine Rekonstruktion der beiden Regierungskrisen in Spielform. Auf Basis der bereits angeführten Zielsetzung, des kurz erläuterten Einblicks in die Theorie sowie der Verwendung unterschiedlicher spieltheoretischer Elemente und Modelle, werden die eine forschungsleitende und zwei weitere Forschungsfragen beantwortet. Im Kern geht es darum, welche spieltheoretische Elemente sich während der Analyse der beiden ausgewählten Regierungskrisen finden lassen und welche Erkenntnisse man daraus ableiten kann. Die Arbeit schließt mit einem Resümee, im Zuge dessen die Erkenntnisse nochmals dargestellt und weitere Forschungsmöglichkeiten aufgezeigt werden. Aus dieser Masterarbeit ergeben sich neben hilfreichen Tipps für die politische Praxis, eben auch weitere Forschungsoptionen für Studierende, die sich sowohl für Politik als auch für strategisches Handeln interessieren. Im Anhang befindet sich ein gesondertes Inhaltsverzeichnis, in welchem klar ersichtlich wird, welcher der beiden Verfasser sich für den jeweiligen Themenbereich hauptverantwortlich zeichnet. Anzumerken ist, dass diese Arbeit im Zuge einer intensiven Zusammenarbeit entstanden ist. This master thesis deals with the applicability of game theory as an analytical technique to political decision-making processes. In recent years, Austria's domestic politics have been shaken more and more frequently by tangible scandals. Especially during the terms of office of the federal governments Kurz I and Kurz II these scandals became more frequent. The following master's thesis, will focus on exactly this research period, the Austrian domestic politics between December 2017 and October 2021. First, it will be examined to what extent game theory is suitable as an analytical technique for the applicability to political facts and subsequently, two government crises from the above research period will be examined for game-theoretical elements. Finally, the defined government crises are reconstructed in game form. The aim of this master thesis is on two different levels. On the one hand, political parties should be able to better anticipate the decisions of their competitors and, based on this, make their respective decisions more target-oriented. On the other hand, political decision-making processes should be made more understandable and transparent for the interested population. The theoretical part at the beginning is devoted to a general overview of game theory. This is followed by essential definitions of terms and the presentation of individual game theory models. Special attention is paid to those areas of game theory that are also applicable to political issues. Practical examples are given in an attempt to provide interested readers with a comprehensible insight into the complex subject of game theory. After the treatment of the theoretical bases the entrance follows into the empirical part of the work. Based on different data, which were collected and evaluated in intensive work, chronological sequences of the two government crises under review are created. These chronological factual representations are then examined for the presence of game-theoretical elements. This results in exciting insights into the actions of the parties involved during the crisis situations. Finally, building on the preliminary work from the theoretical part and the surveys in the empirical part, the two government crises are reconstructed in game form. Based on aforementioned objectives, the briefly explained insight into the theory, and the use of various game-theoretical elements and models, the one research question and two further research questions are answered. In essence, it is about which game-theoretical elements can be found during the analysis of the two selected government crises and which insights can be derived from them. The thesis concludes with a résumé, in the course of which the findings are presented again and further research possibilities are pointed out. This master thesis provides helpful tips for political practice as well as further research options for students who are interested in politics and strategic action. In the appendix there is a separate table of contents, which clearly shows which of the two authors is mainly responsible for the respective topic. It should be noted that this work was developed in the course of an intensive collaboration. Abweichender Titel laut Übersetzung der Verfasserin/des Verfassers Masterarbeit Wien, FH Campus Wien 2022

This paper considers the minimax design of two-dimensional (2D) finite impulse response (FIR) half-band filters. First, the design problem is formulated in a matrix form, where the half-band constraints are expressed as a pair of matrix equations. By matrix transformations, the constrained minimax problem is transformed into an unconstrained one. Then, we propose an efficient iterative reweighted least squares (IRLS) algorithm to solve this problem. The weighted least squares (WLS) subproblems arising from the IRLS algorithm are solved using a generalized conjugate gradient (GCG) algorithm. Moreover, the GCG algorithm is guaranteed to converge in a finite number of iterations. In the proposed algorithm, the design coefficients of filters are solved in their matrix form, leading to a great saving in computations and memory space. Design examples and comparisons with existing methods are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

[EN] Let A, B is an element of C-nxn with ind(A) = k and ind(B) = s and let L-B = (BB)-B-2(sic). A new condition (C-s,C-*): R(A(k)) boolean AND N((B-s)*) = {0} and R(B-s) boolean AND N((A(k))*) = {0}, is defined. Some new characterizations related to core-EP inverses are obtained when B satisfies condition (C-s,C-*). Explicit expressions of B(sic) and BB(sic) are also given. In addition, equivalent conditions, which guarantee that B satisfies condition (C-s,C-*), are investigated. We proved that B satisfies condition (C-s,C-*) if and only if L-B has a fixed matrix form. As an application, upper bounds for the errors parallel to B(sic) - A(sic)parallel to/parallel to A(sic)parallel to and parallel to BB(sic) - AA(sic)parallel to are studied. (c) 2021 Elsevier B.V. All rights reserved., The authors thank the Editor and Reviewers sincerely for their constructive comments and suggestions which have improved the quality of the paper. This research is supported by the National Natural Science Foundation of China (Nos. 11771076, 11871145), the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX18 -0053), the China Scholarship Council (File No. 201906090122). The third author is partially supported by Ministerio de Economia y Competitividad of Spain (grant Red de Excelencia MTM2017-90682-REDT) and partially supported by Universidad de Buenos Aires, Argentina. EXP-UBA: 13.019/2017, 20020170100350BA

This paper presents the dynamic model of multibody systems driven by electric motors, the so-called electromechanical systems. The mechanical systems considered in this study include an open loop and/or a closed loop, a full-actuated and an under-actuated one. The dynamic model of this electromechanical systems is established in matrix form by applying the Lagrangian equation with and without multipliers and substructure method. With this approach it is easy to obtain the differential equation of motion of the electro-mechanical systems based on the corresponding differential equations of the purely available mechanical system. These obtained equations describe the electromechanical systems in engineering better in case the systems are purely described by mechanical equations. The differential equations of serial and parallel manipulators, slider-crank mechanism, and overhead crane driven by electric motors are established as illustrated examples. In addition, a simplified dynamic model obtained by neglecting of current variation is also validated by numerical simulations.

Proton irradiation induced Nb redistribution in Zr-xNb alloys (x = 0.4, 0.5, 1.0 wt%) has been investigated using scanning transmission electron microscopy/energy dispersive X-ray spectroscopy (STEM/EDS). Zr-xNb alloys are mainly composed of Zr matrix, native Zr–Nb–Fe phases, and β-Nb precipitates. After 2 MeV proton irradiation at 350 °C, a decrease of Nb content in native precipitates, as well as irradiation-induced precipitation of Nb-rich platelets (135 ± 69 nm long and 27 ± 12 nm wide) were found. Nb-rich platelets and Zr matrix form the Burgers orientation relationship, [ 1 1 ¯ 1 ]//[ 2 1 ¯ 1 ¯ 0 ] and (011)//(0002). The platelets were found to be mostly coherent with the matrix with a few dislocations near the ends of the precipitate. The coherent strain field has been measured in the matrix and platelets by the 4D-STEM technique. The growth of Nb-rich platelets is mainly driven by coherency and dislocation-induced strain fields. Irradiation may both enhance the diffusion and induce segregation of interstitial Nb to the ends of the irradiation induced platelets, further facilitating their growth.

Typical configuration of an unmanned towed underwater system (UTUS) was described and advantages of using this type of marine equipment for shallow depth works were outlined. A list of basic operating modes of the UTUS which are key modes for design calculations of the system was determined. Basic requirements to the design and construction of a competitive UTUS for shallow water areas have been formed. The main requirements include the need for high-performance underwater technologies and the use of state-of-the-art computer research and design software. The need to maximize use of materials, parts and units that are commercially available as components for the UTUS was also indicated. Expediency and possibility of applying the systems approach methodology at early stages of the UTUS design were shown. Equations of existence were formulated in a matrix form for the UTUS components which make it possible to check engineering solutions for compliance with the requirements of the Requirements Specification already at the stages of technical proposal and sketch design. Structural, power, information and operational characteristics of the UTUS components were used as the compliance criteria. Sequence of the design works was completed in a form of a generalized design algorithm that implements the systems approach using modern computer technologies and equations of the UTUS existence. The developed algorithm allows the designer to check requirements of the Requirements Specification already at the early stages of the UTUS design and forms a scientifically substantiated methodological basis for creation of competitive underwater equipment

In this paper, we propose a new matrix form to generate all 3 × 3 involutory and MDS matrices over F 2 m and prove that the number of all 3 × 3 involutory and MDS matrices over F 2 m is ( 2 m − 1 ) 2 ⋅ ( 2 m − 2 ) ⋅ ( 2 m − 4 ) , where m > 2 . Moreover, we give 3 × 3 involutory and MDS matrices over F 2 3 , F 2 4 and F 2 8 defined by the irreducible polynomials x 3 + x + 1 , x 4 + x + 1 and x 8 + x 7 + x 6 + x + 1 , respectively, by considering the minimum XOR count, which is a metric used in the estimation of hardware implementation cost. Finally, we provide the maximum number of 1s in 3 × 3 involutory MDS matrices.

In this work, we present a solution of the Boussinesq equation, which models shallow water waves. A powerful inverse scattering approach of Deift–Tomei–Trubowitz was published in 1982 for solving this equation in the Schwartz class. We rewrite the corresponding Lax pair in a matrix form and show that a recently developed theory of evolutionary nodes is applicable. As a result, we can locally solve this equation with analytic initial conditions on the line, providing a formula for the tau function, which defines where the solutions exist. More generally, arbitrary analytic solution is shown to arise from a vessel.

A complete mathematical model for measuring the parameters of the scattering matrix for a measurement object [Sx] in the form of a four-port network is developed, in which the mathematical model of the eight-port error is described by 16 parameters of the scattering matrix [E]. In addition, in comparison with the 12-parameter model of the eight-port error network, four parameters are included, which allow taking into account leaks, parasitic transmissions of microwave modules under study (microwave microassemblies). Due to the use of matrix analysis methods, the equations in matrix form are obtained that connect the matrices of the measurement object [Sи] and the actual values of the matrix parameters [Sx], with the aim of enabling the solution of these equations instead of the scattering matrix [E] to use a transmition matrix [T] in the form of cellular matrices [Taa], [Tab], [Tba], [Tbb].

Thermal behavior of integrated passive components has become an important issue when designing these components. This paper presents the thermal modeling of a multilayer integrated LC filter used in DC-DC step-down converter for temperature distribution calculation. The approach used for this analysis is based on thermal equivalent circuit. Temperature distribution is obtained from algebraic equation, which is in vector and matrix form. The results of analytical calculation are compared with simulation results from finite element method. These results showed a good correlation.

OBJECTIVES: Research have identified large individual variation in physiological response to diet, which has led to more focused investigations in precision nutrition. One approach towards personalized nutrition is to identify groups of differential responders, so called metabotypes (i.e., clusters of individuals with similar metabolic profiles and/or regulation). Metabotyping has previously been addressed using matrix decomposition tools like principal component analysis (PCA) on data organized in matrix form. However, metabotyping using data from more complex experimental designs, involving e.g., repeated measures over time or multiple treatments (tensor data), requires new methods. METHODS: We developed a workflow for detecting metabotypes from experimental tensor data. The workflow is based on tensor decomposition, specifically PARAFAC which is conceptually similar to PCA but extended to multidimensional data. Metabotypes, based on metabolomics data were identified from PARAFAC scores using k-means clustering and validated by their association to anthropometric and clinical baseline data. Additionally, we evaluated the robustness of the metabotypes using bootstrapping. Furthermore, we applied the workflow to identify metabotypes using data from a crossover acute post-prandial dietary intervention study on 17 overweight males (BMI 25–30 kg/m2, 41–67 y of age) undergoing three dietary interventions (pickled herring, baked herring and baked beef), measuring 80 metabolites (from GC-MS metabolomics) at 8 time points (0–7h). RESULTS: We identified two metabotypes characterized by differences in amino acid levels, predominantly in the beef diet, that were also associated with creatinine (p = 0.007). The metabotype with higher postprandial amino acid levels was also associated with higher fasting creatinine compared to the other metabotype. CONCLUSIONS: The results stress the potential of PARAFAC to discover metabotypes from complex study designs. The workflow is not restricted to our data structure and can be applied to any type of tensor data. However, PARAFAC is sensitive to data pre-processing and further studies where differential metabotypes are related to clinical endpoints are highly warranted. FUNDING SOURCES: This work has been supported by the Swedish Foundation for Strategic Research and Formas, which is gratefully acknowledged.

Dynamic models play an important role in parallel manipulators simulation and control. Mainly in the later case, the efficiency of the involved computations is of paramount importance, because manipulator real-time control is usually necessary (Zhao & Gao, 2009). The dynamic model of a parallel manipulator operating in free space can be represented in Cartesian coordinates by a system of nonlinear differential equations, which may be written in matrix form as       f x G x x x V x x I          , (1)

Definition of frame-invariant Soret coefficients for ternary mixtures The definition of the Soret coefficient of a binary mixture includes a concentration prefactor, x(1-x) when mol fraction x is used, or w(1-w) when mass fraction w is used. In this presentation the physical reasons behind this choice are reviewed, emphasizing that the use of these prefactors makes the Soret coefficient invariant upon change in the reference frame, either mass or molar. Then, it will be shown how this invariance property can be extended to ternary mixtures by using an appropriate concentration prefactor in matrix form. The presentation will be completed with some considerations of general non-isothermal diffusion fluxes, binary limits of the concentration triangle, selection of the dependent concentration in a ternary mixture, and, finally, extension to multi-component mixtures.References[1] J. M. Ortiz de Zarate. Definition of frame-invariant thermodiffusion and Soret coefficients for ternary mixtures. Eur. Phys. J. E 42(2019), 43

Mass transfer of protectant chemicals is a fundamental aspect of cryopreservation and freeze drying protocols. As such, mass transfer modeling is useful for design of preservation methods. Cell membrane transport modeling has been successfully used to guide design of preservation methods for isolated cells. For tissues, though, there are several mass transfer modeling challenges that arise from phenomena associated with cells being embedded in a tissue matrix. Both cells and the tissue matrix form a barrier to the free diffusion of water and protective chemicals. Notably, the extracellular space becomes important to model. The response of cells embedded in the tissue is dependent on the state of the extracellular space which varies both spatially and temporally. Transport in the extracellular space can also lead to changes in tissue size. In this chapter, we describe various mass transfer models that can be used to describe transport phenomena occurring during loading of tissues with protective molecules for cryopreservation applications. Assumptions and simplifications that limit the applicability of each of these models are discussed.

A spectral collocation method is developed to solve a nonlinear Caputo fractional differential system. The main idea is to solve the corresponding system of weakly singular nonlinear Volterra integral equations (VIEs). The convergence analysis in matrix form shows that the presented method has spectral convergence. Numerical experiments are carried out to confirm theoretical results.

The issues of the interaction of sea and land transport during the transportation of perishable goods are especially in demand at present in connection with the active development of intermodal transport. In addition, due to the rapidly changing specifics of the transport and logistics infrastructure in ports and terminals, the organization of transportation of perishable goods, which are especially vulnerable in terms of quality, requires new approaches and methods. The paper notes the high importance of preliminary preparation for the process of interaction between marine and land transport by operators of marine and land transport. On the part of the marine transport operator, it is advisable to focus on the pre-contractual work and clarification of the conditions for the formation of the freight rate; on the part of the land transportation operator, in the process of preliminary preparation, the state of the transport network for transporting refrigerated cargo near the port is of great importance. The paper proposes two new indicators for assessing the state of the transport network for the transportation of refrigerated goods. At the end of the paper, a model of the interaction of sea and land transport during the transportation of perishable goods with the expression of the multitude of cargo flows of perishable goods in the port through the matrix form is presented.

Data analytics allows an analyst to gain insight into underlying populations through the use of various computational approaches, including Monte Carlo methods. This paper discusses an approach to apply Monte Carlo methods to hedonic games. Hedonic games have gain popularity over the last two decades leading to several research articles that are concerned with the necessary, sufficient, or both conditions of the existence of a core partition. Researchers have used analytical methods for this work. We propose that using a numerical approach will give insights that might not be available through current analytical methods. In this paper, we describe an approach to representing hedonic games, with strict preferences, in a matrix form that can easily be generated; that is, a hedonic game with randomly generated preferences for each player. Using this generative approach, we were able to create and solve, i.e., find any core partitions, of millions of hedonic games. Our Monte Carlo experiment generated games with up to thirteen players. The results discuss the distribution form of the core size of the games of a given number of players. We also discuss computational considerations. Our numerical study of hedonic games gives insight into the underlying properties of hedonic games., Comment: 44 pages

Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang-Mills theory. We illustrate the procedure for the toy electroweak model., 16 pages, 2 figures, changed equation numbering

In this paper, we give quadratic approximation of generalized Tribonacci sequence $\{V_{n}\}_{n\geq0}$ defined by Eq. (\ref{eq:7}) and use this result to give the matrix form of the $n$-th power of a companion matrix of $\{V_{n}\}_{n\geq0}$. Then we re-prove the cubic identity or Cassini-type formula for $\{V_{n}\}_{n\geq0}$ and the Binet's formula of the generalized Tribonacci quaternions., Comment: 10 pages

espanolEn este articulo, se muestra una aplicacion y avance al metodo que permite encontrar de manera simple los coeficientes constantes que se requieren en la solucion de una ecuacion diferencial con la estructura de Cauchy-Euler, presentada y dada a conocer en [1]. Aqui veremos la forma de construccion de los polinomios caracteristicos, utilizando el metodo mencionado anteriormente como base; con una serie de ecuaciones, matrices y metodos novedosos para resolver este tipo de EDO y, sobre todo, muy practicas para la solucion de la ecuacion de orden superior. La idea es presentar una estructura o metodologia en forma matricial que permita resolver de manera practica la ecuacion diferencial de orden superior con la estructura de Cauchy-Euler. EnglishIn this article application and advance is given to the method that allows to find in a simple way the constant coefficients that are required in the solution of a differential equation with the structure of Cauchy-Euler, presented and made known in [1]. Here we will see the construction form of the characteristic polynomials, using the aforementioned method as a basis; with a series of equations, matrices and novel methods to solve this type of ODEs and, above all, very practical for the equation of a much higher order. The idea is to present a structure or methodology in matrix form that allows to solve in a practical way differential equation of higher order with Cauchy-Euler structure.

We study the strategic interaction between a new good producer and a remanufacturer who use advertising campaigns to compete for a dominant share of the market for a certain good. Each firm chooses one of three possible strategies for running its advertising campaign. The two rival firms care only about capturing a dominant share of the relevant market. Hence, if a firm expects to capture dominant market share with probability p є [0, 1], then its payoff in the game we study is also p. Our analysis leads to four results. First, we provide the normal form representation of the game between the new good producer and the remanufacturer. Second, we specify the game in matrix form. Third, we indicate what happens at each stage of the elimination of strictly dominated strategies. Finally, we show that the iterated elimination of strictly dominated strategies yields a clear and unique prediction about the outcome of the advertising game.

Precision machine tools are usually installed on foundations via supporting elements. In this configuration, errors because of inappropriate support lengths (level error) have to be adjusted during the installation to align the level of the machine tool. Consequently, a quantitative indication of level errors is a necessity for levelling works. Therefore, a model-based approach for level condition monitoring, which can identify level errors, is proposed. In the model, machine supports are modeled as linear springs. The relationship between the level error and preload distribution is modeled in matrix form. This report verifies the fundamentals of the proposed approach through experiments performed on a machining center.

Research is of little use if its results are not effectively communicated. Data visualised in graphs (and tables) are key components in any scientific report, but their design leaves much to be desired. This viewpoint focuses on graph design, following two general principles: clear vision and clear understanding. Clear vision is achieved by maximising the signal to noise ratio. In a graph, the signal is the data in the form of symbols, lines or other graphic elements, and the noise is the support structure necessary to interpret the data. Clear understanding is achieved when the story in the data is told effectively, through organisation of the data and use of text. These principles are illustrated by original and improved graphs from recent publications, completed by tutorial material online (appendices, web pages and film clips). The popular matrix form (multiple graphs in one frame) is discussed as a special case. Differences between publication (including the proofing stage) and presentation are outlined. Suggestions are made for better peer review and processing of graphs in the publication stage.

This paper presents a new formulation for analyzing a beam on elastic supports traveling on irregular profiles. The model is a first approximation of a passenger railway vehicle car body. The main difference with previous works is the use of a complex modulus to represent structural damping rather than relying on equivalent viscous terms. The formulation groups rigid body modes with flexible modes and proposes a matrix form that is easy to interpret and solve in the frequency domain. Comfort indexes are readily obtained from weighted response spectral densities. The model is used to assess the influence of structural damping and stiffness on comfort. It will be shown that the evolution of comfort with stiffness is non-monotonic and, therefore, comfort does not always improve as stiffness increases.