Crystallographic and spectroscopic studies have been performed of structures, coordination and chemical bonding for series of trivalent metal ions solvated by two oxygen-coordinating solvents, water and dimethyl sulfoxide (DMSO). The hydrated scandium(III) and lanthanoid(III) ions, La to Lu, are surrounded by tricapped trigonal prisms of aqua ligands in the isomorphous series of trifluoromethanesulfonates, [M(H2O)n](CF3SO3)3. For the smallest ions, M = Er, Tm, Yb, Lu, Sc, the hydration numbers decrease, n = 8.96(5), 8.8(1), 8.7(1), 8.5(1), 8.0(1), respectively, with decreasing size of the ion. The crystal structures at ambient temperature indicate randomly distributed vacancies of the capping oxygen atoms, and 2H solid-state NMR of the diamagnetic [M(H2O)n](CF3SO3)3, M = Sc, Lu, Y and La compounds revealed increasing mobility of the water ligands in the coordination sphere with increasing temperature, also for the fully nonahydrated LaIII and YIII ions. The stretching force constants of the Ln-O bonds, evaluated from vibrational spectroscopy, increased from 0.81 to 1.16 N cm-1 for the Ln-6O trigonal prism in a smooth correlation with the bond distances from La to Lu. For the capping Ln-3O bonds the increase from 0.49 to 0.65 N cm-1 reflects the increased ligand-ligand repulsion with decreasing ion size. This is also the reason for the water deficiency of the Er, Tm, Yb, Lu and Sc salts, and for [Sc(H2O)8.0](CF3SO3)3 the repulsion induced a phase transition at about 185 K that, by low temperature crystallography, was found to distort the coordination of water molecules toward a monocapped trigonal prism around the scandium(III) ion. All crystal structures of the octakis(dimethyl sulfoxide)lanthanoid(III) iodides comprise discrete [Ln(dmso)8]3+ complexes surrounded by iodide ions. The lanthanum(III) and praseodymium(III) compounds crystallize in the orthorhombic space group Pbca with more efficient packing than for the heavier and smaller ions in the lanthanoid series, which crystallize in the monoclinic space group P21/n. The group 13 metal ions, aluminium(III), gallium(III), indium(III), thallium(III), and also scandium(III) of group 3, form crystalline hexakis(dimethyl sulfoxide) solvates in the space group R 3, with octahedral MO6 coordination entities, which are increasingly compressed along one threefold axis for increasing ionic size. EXAFS measurements on the solvated ions display similar M-O bond distances in dimethyl sulfoxide solution as in the solid solvates. For all the solid dimethyl sulfoxide solvates the strength and nature of the metal-oxygen bond has been evaluated by normal coordinate analysis of vibrational spectra, and correlated with the S-O stretching vibrational mode. Distortions from regular octahedral six coordination are discussed for the hydrated isoelectronic soft mercury(II) and thallium(III) ions in the solid bisaquamercury(II) and trisaquatallium(III) trifluoromethanesulfonates, in terms of pseudo Jahn-Teller effects (PJTE). Mercury(II), generally more strongly influenced by PJTE distortions, displays a 2 + 4 Hg-O coordination forming chains that are held together in sheets by hydrogen bonds and in layers by van der Waals interactions, which explain the fragile structure of the crystals.

Large displacement and large strain problems of mechanical systems can be solved mainly by four methods. These are Floating Frame of Reference, Incremental Finite Element, Large Rotation Vector and Absolute Nodal Coordinate Formulations (ANCF). Due to exact rigid body representation, simple mass matrix structure and non-incremental formulation, ANCF is more convenient in analyzing flexible multibody systems. However, it is limited to problems with regular boundaries, currently. The aim of the thesis is to improve the current ANCF in order to handle various problems with irregular boundaries. For this purpose, firstly meshfree ANCF has been developed to analyze flexible multibody systems. Verification of the developed meshfree formulation has been performed for beam type structures and accurate results have been obtained. Then, &ldquo / ANCF with Virtual Element Mapping Method&rdquo / has been proposed to overcome the boundary problems of the current formulations. The proposed method has been implemented to plane stress, plane strain, plate/shell and 3D solid finite elements. Verification of the proposed method has been performed by using the patch test problems available in the literature. Besides, it has been verified by various flexible multibody problems with large deformations. Additionally, shape function polynomials for thin plate assumption have been derived. It is observed that developed formulations and methods can be useful not only for flexible multibody systems but also for structural mechanics problems subjected to large deformations and/or rotations. The proposed methods and formulations are more efficient than the current formulations in the literature due to extended shape limits of finite elements.

This thesis presents various studies on energy efficient design of wireless networks. It starts with a survey on recent shortest path based energy efficient routing algorithms developed for ad hoc and sensor networks, making a comprehensive classification for these algorithms. In addition to energy efficient design, sustainable and environmentally friendly deployment of wireless networks demands increased use of renewable energy. However, this calls for novel design principles to efficiently utilize the variation in the availability of the energy. The thesis continues with an investigation of state-of-the-art resource management and scheduling algorithms developed for energy harvesting wireless sensor networks. Building on the stateof- the-art, the main contribution of this thesis is to formulate and solve a utility maximizing scheduling problem in a multiuser broadcast channel with an energy harvesting transmitter. The goal is to determine the optimal power and time allocations to users between energy arrivals. The structural properties of the problem are analyzed, and its biconvexity is proved. A Block Coordinate Descent (BCD) based algorithm is developed to obtain the optimal solution. Two simple and computationally scalable heuristics, PTF and ProNTO, which mimic the characteristics of the optimal policy, are proposed. Finally, an online algorithm, PTF-On,that will bypass the need for offline knowledge about the energy harvesting statistics, is developed. PTF-On uses a Kalman filter based energy harvesting prediction algorithm, developed in this thesis, to predict the energy that will arrive in the future.

This thesis considers regularized block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. I review some of its interesting examples and propose a generalized block coordinate descent (BCD) method. The generalized BCD uses three different block-update schemes. Based on the property of one block subproblem, one can freely choose one of the three schemes to update the corresponding block of variables. Appropriate choices of block-update schemes can often speed up the algorithm and greatly save computing time. Under certain conditions, I show that any limit point satisfies the Nash equilibrium conditions. Furthermore, I establish its global convergence and estimate its asymptotic convergence rate by assuming a property based on the Kurdyka-{\L}ojasiewicz inequality. As a consequence, this thesis gives a global linear convergence result of cyclic block coordinate descent for strongly convex optimization. The proposed algorithms are adapted for factorizing nonnegative matrices and tensors, as well as completing them from their incomplete observations. The algorithms were tested on synthetic data, hyperspectral data, as well as image sets from the CBCL, ORL and Swimmer databases. Compared to the existing state-of-the-art algorithms, the proposed algorithms demonstrate superior performance in both speed and solution quality.

In this thesis, the measurement uncertainty of Coordinate Measuring Machine (CMM) is analysed and software is designed to simulate this. Analysis begins with the inspection of the measurement process and structure of the CMMs. After that, error sources are defined with respect to their effects on the measurement and then an error model is constructed to compensate these effects. In other words, systematic part of geometric, kinematic and thermal errors are compensated with error modelling. Kinematic and geometric error model is specific for the structure of CMM under inspection. Also, a common orthogonal kinematic model is formed and with using the laser error data of the CMM and error maps of the machine volume is obtained. Afterwards, the models are compared with each other by taking the difference and ratio. The definition and compensation of the systematic errors leave the uncertainty of measurements for analysing. Measurement uncertainty consists of the uncompensated systematic errors and random errors. The other aim of the thesis is to quantify these uncertainties with using the different methods and to inspect the success of these methods. Uncertainty budgeting, comparison, statistical evaluation by designing an experiments and simulation methods are examined and applied to the CMM under inspection. In addition, Virtual CMM software is designed to simulate the task specific measurement uncertainty of circle, sphere and plane without using the repeated measurements. Finally, the performance of the software, highly depending on the mathematical modelling of machine volume, is tested by using actual measurements.

Coordinate Measuring Machines (CMMs) have been widely used in industry in order to determine the form / dimensional tolerances of workpieces with very complicated geometrical shapes. Therefore, CMM is an important tool during the manufacturing and quality control phases. Workpiece to be measured on a CMM is probed via touch trigger probe through its stylus tip. In other words, by virtue of the touch trigger probes CMM can acquire the dimensional data of the workpiece that is to be measured. Therefore the probe has become the most vital and fundamental part of the CMM. In this thesis, a novel type of touch trigger probe / scanning probe is proposed. The proposed probe can also be used as a scanning probe for different applications. The main purpose of this thesis is to develop a novel type of touch trigger / scanning probe that has different kinematic stage and sensing stage than the other probes currently used in the industry. Giant Magnetoresistive (GMR) sensors are used for building the sensing stage of the proposed probe. GMR sensors are selected due to their outstanding sensitivity to small disturbances. Furthermore, in order to test the proposed probe / an anvil gauge setup is designed and proposed in this study. Finally, proposed probe is tested on a three-axis computer controlled electrical discharge machine (EDM), and the results acquired from those experiments are discussed.

Οι ροές φλεβών άνωσης παρουσιάζουν μεγάλο ενδιαφέρον στην περιβαλλοντική υδραυλική και στη μηχανική των ρευστών, επειδή εμφανίζονται σε αρκετά φαινόμενα που σχετίζονται με τη διάθεση υγρών αποβλήτων ή θερμικών απορρίψεων σε υδάτινους αποδέκτες καθώς επίσης και την εκπομπή αερίων ενώσεων από καμινάδες στην ατμόσφαιρα. Στην παρούσα Διδακτορική Διατριβή μελετήθηκε η ροή κεκλιμένης δισδιάστατης ή κυκλικής ανωστικής φλέβας εντός ακίνητου ή κινούμενου αποδέκτη και η αλληλεπίδραση μεταξύ ανωστικών φλεβών. Στα υπάρχοντα μαθηματικά μοντέλα, ο υπολογισμός του πεδίου ροής και διάχυσης μιας κεκλιμένης ανωστικής φλέβας πραγματοποιείται επιλύοντας το σύστημα των διαφορικών εξισώσεων της συνεχείας, της ορμής και της διατήρησης της μάζας του ιχνηθέτη, για τη μέση ροή, σε ένα καρτεσιανό ή κυλινδρικό σύστημα συντεταγμένων. Με αυτό τον τρόπο όμως, παραλείπονται όροι από τις εξισώσεις που προσδίδουν μεγαλύτερη ακρίβεια. Ακόμη, το φαινόμενο της αποκόλλησης μαζών από την ανωστική φλέβα έχει μεν παρατηρηθεί σε πειραματικές εργασίες διαφόρων ερευνητών αλλά δεν έχει προσδιοριστεί ποσοτικά. Μία ακόμη αδυναμία που χαρακτηρίζει τα υπάρχοντα μαθηματικά μοντέλα, είναι ότι θεωρούν τον αποδέκτη απεριορίστων διαστάσεων με συνέπεια τα αποτελέσματά τους να μην ακολουθούν τα αντίστοιχα πειραματικά αποτελέσματα, τα οποία φέρουν την επιρροή των ορίων, αφού πρακτικά δεν γίνεται να πραγματοποιηθούν σε αποδέκτες απεριορίστων διαστάσεων. Η παρούσα Διατριβή επιχειρεί να συμβάλλει στη βελτίωση των παραπάνω αδυναμιών, προτείνοντας τη μαθηματική περιγραφή της ελεύθερης κεκλιμένης τυρβώδους ανωστικής φλέβας σε ένα καμπυλόγραμμο ορθογώνιο ή κυλινδρικό σύστημα συντεταγμένων, ώστε να επιτευχθεί καλύτερη ακρίβεια στον υπολογισμό των μέσων χαρακτηριστικών της ροής. Επίσης, αναπτύσσεται ένα μαθηματικό μοντέλο, το οποίο προσομοιώνει τη διαφυγή των μαζών που αποκολλώνται από το σώμα της ανωστικής φλέβας, και όπως φαίνεται, τα δύο αυτά στοιχεία επηρεάζουν τόσο την τροχιά της φλέβας όσο και την αραίωση. Στο σημείο αυτό, η παρούσα Διατριβή χρησιμοποιεί τη μέθοδο της συμμετρικής εικονικής πηγής για την απόκτηση λύσης του προβλήματος σε ημίχωρο. Θεωρείται, λοιπόν, κατοπτρικά ως προς το όριο όμοια εικονική πηγή με την πραγματική, ανωστική φλέβα, η οποία αλληλεπιδρά δυναμικά με την ανωστική φλέβα της πραγματικής πηγής. Τέλος, τα ανωτέρω συνδυάζονται στην ανάπτυξη ενός μοντέλου, το οποίο υπολογίζει τα χαρακτηριστικά του πεδίου μέσης ροής και διάχυσης από την αλληλεπίδραση N κατακορύφων ανωστικών φλεβών σε διάταξη τύπου ροζέτας εντός ήρεμου αποδέκτη. Το μοντέλο αυτό παρέχει ακρίβεια 2ης τάξης. Η παρούσα διατριβή αναπτύσσεται σε έξι κεφάλαια. Στο πρώτο Κεφάλαιο, πραγματοποιείται μια εισαγωγή στο αντικείμενο της Διατριβής. Αναφέρονται τα πεδία στα οποία συναντώνται φαινόμενα ροών από ανωστικές φλέβες και η πρακτική σημασία τους. Επίσης, αναφέρονται οι στόχοι οι οποίοι επιδιώκονται μέσω της Διατριβής. Το δεύτερο Κεφάλαιο, περιέχει βιβλιογραφική ανασκόπηση, στην οποία αναφέρονται τα κυριότερα μαθηματικά μοντέλα για τις περιπτώσεις των ελευθέρων και των πολλαπλών κυκλικών ή δισδιάστατων ανωστικών φλεβών. Επίσης, παρουσιάζονται οι σημαντικότερες διαθέσιμες ερευνητικές εργασίες διεξαχθέντων συναφών πειραμάτων, των οποίων οι μετρήσεις χρησιμοποιούνται στον έλεγχο των αποτελεσμάτων, τα οποία προκύπτουν από την εφαρμογή των μαθηματικών μοντέλων που αναπτύσσονται στην παρούσα Διατριβή. Στο τρίτο Κεφάλαιο, αναπτύσσονται τα υποστηρικτικά μοντέλα, τα οποία ενσωματώνονται στο γενικότερο μαθηματικό μοντέλο υπολογισμού των κεκλιμένων ανωστικών φλεβών και στο μοντέλο της αλληλεπίδρασής τους. Αρχικώς, κατασκευάζεται το σύστημα το καμπυλογράμμων ορθογωνίων και κυλινδρικών συντεταγμένων και διατυπώνονται οι εξισώσεις της συνεχείας, της ορμής και της διατήρησης της μάζας του ιχνηθέτη για τη μέση ροή στο αντίστοιχο σύστημα. Στην συνέχεια, περιγράφεται η ανάπτυξη του μοντέλου για τον πυρήνα της Ζώνης Εγκατάστασης της Ροής, το οποίο υπολογίζει τις πραγματικές εγκάρσιες κατανομές των ταχυτήτων και των συγκεντρώσεων ξεκινώντας από την έξοδο του ακροφυσίου έως το πέρας του πυρήνα. Τέλος, αναπτύσσεται το μαθηματικό μοντέλο, το οποίο περιγράφει τη διαφυγή των μαζών που αποκολλώνται από το πεδίο ροής μιας κεκλιμένης δισδιάστατης ή κυκλικής τυρβώδους ανωστικής φλέβας. Στο τέταρτο Κεφάλαιο, παρουσιάζεται ένα ολοκληρωμένο μαθηματικό μοντέλο για μια κεκλιμένη δισδιάστατη ή κυκλική τυρβώδη ανωστική φλέβα σε ήρεμο ή κινούμενο αποδέκτη, το οποίο ενσωματώνει τα επί μέρους μοντέλα του τρίτου Κεφαλαίου. Το μοντέλο, συγκρίνεται με τα διαθέσιμα πειραματικά δεδομένα της διεθνούς βιβλιογραφίας και ταυτοχρόνως ρυθμίζεται η προσομοίωση της διαφυγής των μαζών που αποκολλώνται. Στο πέμπτο Κεφάλαιο εξετάζεται η αλληλεπίδραση μεταξύ τυρβωδών ανωστικών φλεβών. Στο πρώτο μέρος του Κεφαλαίου προτείνεται ένα μοντέλο 2ης τάξης, το οποίο υπολογίζει τα χαρακτηριστικά του μέσου πεδίου ροής και διάχυσης από την αλληλεπίδραση Ν κατακορύφων κυκλικών ανωστικών φλεβών από διαχύτη τύπου ροζέτας. Στο δεύτερο μέρος, μελετάται η δυναμική αλληλεπίδραση μεταξύ ανωστικών φλεβών. Αναπτύσσεται το σύστημα των εξισώσεων, το οποίο ενσωματώνει τη δυναμική αλληλεπίδραση, και αντιμετωπίζεται η ύπαρξη στερεών ορίων στο πεδίο ροής ανωστικής φλέβας μέσω της αλληλεπίδρασης των ανωστικών φλεβών από την πραγματική και τη συμμετρική εικονική της πηγή. Στο έκτο Κεφάλαιο, παρουσιάζονται τα συμπεράσματα, τα οποία προκύπτουν από την εφαρμογή των διαφόρων μαθηματικών μοντέλων της Διατριβής, τα οποία εν συντομία, είναι τα εξής: • Αναπτύσσεται ένα μαθηματικό μοντέλο, το οποίο υπολογίζει με πολύ μεγάλη ακρίβεια την κεκλιμένη δισδιάστατη ή κυκλική τυρβώδη ανωστική φλέβα, για αρχικές γωνίες κλίσης -75° ≤ θ0 ≤ 90°. • Η προσομοίωση της διαφυγής των μαζών, που αποκολλώνται από την ανωστική φλέβα, προσεγγίζει ακριβέστερα την τροχιά των κεκλιμένων φλεβών, όπως αυτή προσδιορίζεται από τις πειραματικές μετρήσεις. • Λόγω έλλειψης πειραματικών δεδομένων για την περίπτωση της κεκλιμένης δισδιάστατης τυρβώδους ανωστικής φλέβας, ο συντελεστής Λ, που χαρακτηρίζει τις αποκολλήσεις, λαμβάνεται ίσος με 0,06, για την περίπτωση όπου θ0 = 0°. • Για την κεκλιμένη κυκλική τυρβώδη ανωστική φλέβα, προτείνεται Λ = 0,34 για -75° ≤ θ0 ≤ -15° και Λ = 0,00 για -15° < θ0 ≤ 90°, δηλώνοντας ότι οι διαφυγές σε αυτές τις γωνίες είναι αμελητέες. • Προβλέπεται με χαρακτηριστική ακρίβεια το εξωτερικό όριο των κεκλιμένων κυκλικών τυρβωδών ανωστικών φλεβών και με ικανοποιητική ακρίβεια η τροχιά, συγκριτικά με τα διαθέσιμα αποτελέσματα των αντιστοίχων πειραμάτων. Η σύγκριση του εσωτερικού ορίου εξαιτίας της ύπαρξης των διαφυγών είναι δυσδιάκριτη και πιθανόν να εμπεριέχει σφάλματα. • Ο υπολογισμός των χαρακτηριστικών της ροής, από την αλληλεπίδραση N κατακορύφων κυκλικών τυρβωδών ανωστικών φλεβών από διαχύτη τύπου ροζέτας εντός ήρεμου αποδέκτη, δίνουν ικανοποιητικά αποτελέσματα συγκρινόμενα με τα υπάρχοντα πειραματικά και θεωρητικά δεδομένα • Η αλληλεπίδραση Ν ομοίων ή διαφορετικών δισδιάστατων ή κυκλικών τυρβωδών ανωστικών φλεβών αντιμετωπίζεται χρησιμοποιώντας τη θεωρία του δυναμικού πεδίου. • Η αντιμετώπιση των εξωτερικών ορίων, χρησιμοποιώντας τη δυναμική αλληλεπίδραση μεταξύ ανωστικών φλεβών δίνει ενθαρρυντικά αποτελέσματα. Τέλος, στα Παραρτήματα περιγράφεται αναλυτικώς η μαθηματική ανάπτυξη του κάθε μοντέλου και δίνονται σε μορφή διαγραμμάτων τα θεωρητικά αποτελέσματα με τα αντίστοιχα πειραματικά δεδομένα για τα διάφορα χαρακτηριστικά των κεκλιμένων κυκλικών ανωστικών φλεβών. / In this Doctoral Thesis a mathematical model that predicts the mean flow and mixing parameters of inclined plane and round turbulent jets in a stationary or moving uniform fluid environment is developed. Also, the interaction of multiple buoyant jets is mathematically examined. The existing mathematical models predict the mean flow and mixing properties of an inclined plane and round turbulent buoyant jets in a uniform stationery or moving environment solving the system of partial differential equations of continuity momentum and tracer conservation of mass written in cartesian or cylindrical coordinates. By this way, the terms that give a better precision are omitted. Also, the escaping masses from the main buoyant jet flow that are experimentally observed are not quantified. Furthermore, these models assume that the receiver is infinite so the predicted properties do not coincide to experimental data. These experimental data are affected by the boundaries as the experiments cannot be conducted in boundless environment. The present Thesis, attempts to improve the aforementioned weaknesses. In this Thesis, a mathematical description of an inclined turbulent plane or round buoyant jet is proposed, where the partial differential equations for continuity, momentum and tracer conservation are written in orthogonal and cylindrical curvilinear coordinates in order to achieve better accuracy of the mean flow and mixing parameters. The escaping masses from the main buoyant jet flow are simulated, and the model can be successfully applied to initial discharge inclinations θ0 from 90° to -75° with respect to the horizontal plane. This is based on the idea that masses may escape from the buoyant jet zones where considerable intermittency occurs and entrainment shows large variations having a very weak, zero or negative mean value and at the same time some buoyant chunks lose their inertia due to reversal motions imposed by the large eddies. Thus, the only governing force on these masses is buoyancy. This complementary approach introduces a concentration coefficient, called Λ, which is calibrated using experimental evidence. This phenomenon is sharper in motionless environment. The present model has incorporated the second-order approach and, regarding the jet-core region, a jet-core model based on the advanced integral model for the production of more correct transverse profiles of the mean axial velocities and mean concentrations than the common Gaussian or top-hat profiles. The partial differential equations for momentum and tracer conservation are written in orthogonal and cylindrical curvilinear coordinates for inclined plane and round buoyant jets, respectively, and they are integrated under the closure assumptions of (a) quasi-linear spreading of the mean flow and mixing fields, and (b) known transverse profile distributions. The integral forms are solved by employing the Runge–Kutta algorithm. This model is applied to predict the mean flow properties (trajectory characteristics, mean axial velocities and mean concentrations) for inclined plane and round buoyant jets. The results predicted are compared with experimental data available in the literature, and the accuracy obtained is more than satisfactory. The best values of Λ were found to be in the range from 0.30 to 0.42, indicating a mean value ± standard deviation of Λ = 0.344 ± 0.053 for -75° ≤ θ0 ≤ -15°. Thus Λ = 0.34 is adopted as the suitable value for all cases of round buoyant jets with -75° ≤ θ0 ≤ -15°, while for the rest range -15° < θ0 ≤ 90° the pertinent value is Λ = 0. For the inclined plane buoyant jets, the available experimental data are rather restricted to only trajectories and concentrations of horizontal discharges, which allow the determination of a suitable value Λ = 0.08. The Entrainment Restriction Approach is employed in interacting round buoyant jets discharged vertically upwards from a rosette type diffuser into a calm environment. Incorporating the second order approach, the prediction of the mean-flow properties achieves better accuracy. The present Thesis solves the interaction of N identical or not inclined turbulent plane or round buoyant jets using the potentional theory. The occurrence of boundaries is handled via the method of symmetric virtual origin. A mirror image to the boundary, which is identical to the real buoyant jet, is assumed that dynamically interacts with the buoyant jet issued form the real source.

Darbe ištirtos ir palygintos dviejų elektrofotografinių mašinų „Xerox DC5000“ ir „Conica Minolta 6500“ spalvų reprodukavimo galimybės. Tyrimas buvo atliekamas dviem spaudos mašinomis po tam tikro spaudų skaičiaus atspausdinant kalibracinį testą (lapą su specialiai spektrofotometrui paruoštais vienodo dydžio įvairių atspalvių kvadratėliais, kuriuose yra skirtingas visų keturių CMYK spalvų rastrinių taškų skaičius), kurio spalvų intensyvumas buvo matuojamas spektrofotometru „Efi ES–1000“. Nustatyta, kad spaudos mašinos „Xerox“ reprodukuojamų spalvų sodris didesnis lyginant su „Minolta“, tai lemia spaudo padengimas laku, kuris sukelia veidrodinį efektą, eliminuojama patenkanti į matavimo prietaisą išsklaidyta šviesa. Nustatytas savikalibracinės sistemos netobulumas bei abiejų mašinų spaudų skaičius, po kurio mašina turi buti kalibruojama. Darbą sudaro 7 dalys: įvadas, literatūros apžvalga, tyrimų metodika, rezultatai ir jų aptarimas, išvados ir rekomendacijos, literatūros sąrašas, priedai. Darbo apimtis – 57 p. teksto be priedų, 3 lentelės, 33 paveikslai, 15 bibliografinių šaltinių. Darbo priedai pridedami darbo pabaigoje. / The research regarding colour reproduction possibilities of two electrographic machines “Xerox DocuColor 5000” and “Conica Minolta Bizhub pro C6500” was made. In it two stamped machines were used, which had to stamp fixed numbers of calibration test (a paper with specially made, same size and various colours quadrants for spectrofotometer, where is different number of all four CMYK bitmap colour dots), which colour intensity was measured with using spaectrofotometer “Efi ES-1000”. The results have shown that “Xerox” machine has larger colour reproduction depth comparing to “Minolta” . This condition is made because of varnish that covers stamp. It creates specular effect and eliminates resolved light that comes to measuring devices. Self calibrating system cracks were discovered as well. Also two machines have to be calibrated after fixed number of stamps. Thesis has 7 parts: Introduction, literature review, research methodology, results, results discussion, conclusion and recommendation, literature list, appendix. Thesis consist of: 57p. text without appendix, 3 tables, 33 pictures, 15 bibliographical.

Computer simulations have emerged as a cost efficient complement to laboratory experiments, as computers have become increasingly powerful. The aim of the present work is to explore the ideas of some state of the art software development practices, and ways in which these can be useful for developing high performance research codes. The introduction of these practices, and the modular designs that they give rise to, raises issues regarding a potential conflict between runtime efficiency on one hand and development efficiency on the other. Flexible software modules, based on mathematical abstractions, will provide support for convenient implementation and modification of numerical operators. Questions still remain about whether such modules will provide the efficiency which is required for high performance applications. To answer these questions, investigations were performed within two different problem domains. The first domain consisted of modular frameworks for the numerical solution of Partial Differential Equations. Such frameworks proved a suitable setting, since several of my research questions revolved around the issue of modularity. The second problem domain was that of symmetry exploiting algorithms. These algorithms are based on group theory, and make ample use of mathematical abstractions from that field. The domain of symmetry exploiting algorithms gave us opportunities to investigate difficulties in combining modularity based on high level abstractions with low level optimizations using data layout and parallelization. In conclusion, my investigation of software development practices for the area of high performance computing has proved very fruitful indeed. I have found that none of the concerns that were raised should lead us to refrain from the use of the practices that I have considered. On the contrary, in the two case studies presented here, these practices lead to designs that perform well in terms of usability as well as runtime efficiency.

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies for these methods. In the first four chapters we focus on four views on the sampling for convex problems, developing and analyzing new state-of-the-art methods using non-standard data sampling strategies. Finally, in the last chapter we present a more flexible framework, which generalizes to more problems as well as more sampling rules. In the first chapter we propose an adaptive variant of stochastic dual coordinate ascent (SDCA) for solving the regularized empirical risk minimization (ERM) problem. Our modification consists in allowing the method to adaptively change the probability distribution over the dual variables throughout the iterative process. AdaSDCA achieves a provably better complexity bound than SDCA with the best fixed probability distribution, known as importance sampling. However, it is of a theoretical character as it is expensive to implement. We also propose AdaSDCA+: a practical variant which in our experiments outperforms existing non-adaptive methods. In the second chapter we extend the dual-free analysis of SDCA, to arbitrary mini-batching schemes. Our method is able to better utilize the information in the data defining the ERM problem. For convex loss functions, our complexity results match those of QUARTZ, which is a primal-dual method also allowing for arbitrary mini-batching schemes. The advantage of a dual-free analysis comes from the fact that it guarantees convergence even for non-convex loss functions, as long as the average loss is convex. We illustrate through experiments the utility of being able to design arbitrary mini-batching schemes. In the third chapter we study importance sampling of minibatches. Minibatching is a well studied and highly popular technique in supervised learning, used by practitioners due to its ability to accelerate training through better utilization of parallel processing power and reduction of stochastic variance. Another popular technique is importance sampling { a strategy for preferential sampling of more important examples also capable of accelerating the training process. However, despite considerable effort by the community in these areas, and due to the inherent technical difficulty of the problem, there is no existing work combining the power of importance sampling with the strength of minibatching. In this chapter we propose the first importance sampling for minibatches and give simple and rigorous complexity analysis of its performance. We illustrate on synthetic problems that for training data of certain properties, our sampling can lead to several orders of magnitude improvement in training time. We then test the new sampling on several popular datasets, and show that the improvement can reach an order of magnitude. In the fourth chapter we ask whether randomized coordinate descent (RCD) methods should be applied to the ERM problem or rather to its dual. When the number of examples (n) is much larger than the number of features (d), a common strategy is to apply RCD to the dual problem. On the other hand, when the number of features is much larger than the number of examples, it makes sense to apply RCD directly to the primal problem. In this paper we provide the first joint study of these two approaches when applied to L2-regularized ERM. First, we show through a rigorous analysis that for dense data, the above intuition is precisely correct. However, we find that for sparse and structured data, primal RCD can significantly outperform dual RCD even if d ≪ n, and vice versa, dual RCD can be much faster than primal RCD even if n ≫ d. Moreover, we show that, surprisingly, a single sampling strategy minimizes both the (bound on the) number of iterations and the overall expected complexity of RCD. Note that the latter complexity measure also takes into account the average cost of the iterations, which depends on the structure and sparsity of the data, and on the sampling strategy employed. We confirm our theoretical predictions using extensive experiments with both synthetic and real data sets. In the last chapter we introduce two novel generalizations of the theory for gradient descent type methods in the proximal setting. Firstly, we introduce the proportion function, which we further use to analyze all the known block-selection rules for coordinate descent methods under a single framework. This framework includes randomized methods with uniform, non-uniform or even adaptive sampling strategies, as well as deterministic methods with batch, greedy or cyclic selection rules. We additionally introduce a novel block selection technique called greedy minibatches, for which we provide competitive convergence guarantees. Secondly, the whole theory of strongly-convex optimization was recently generalized to a specific class of non-convex functions satisfying the so-called Polyak- Lojasiewicz condition. To mirror this generalization in the weakly convex case, we introduce the Weak Polyak- Lojasiewicz condition, using which we give global convergence guarantees for a class of non-convex functions previously not considered in theory. Additionally, we give local convergence guarantees for an even larger class of non-convex functions satisfying only a certain smoothness assumption. By combining the two above mentioned generalizations we recover the state-of-the-art convergence guarantees for a large class of previously known methods and setups as special cases of our framework. Also, we provide new guarantees for many previously not considered combinations of methods and setups, as well as a huge class of novel non-convex objectives. The flexibility of our approach offers a lot of potential for future research, as any new block selection procedure will have a convergence guarantee for all objectives considered in our framework, while any new objective analyzed under our approach will have a whole fleet of block selection rules with convergence guarantees readily available.