Reinforcement Learning Solution for Unit Commitment Problem Considering Minimum Start Up and Shut Down Times

Unit Commitment Problem (UCP) in power system refers to the problem of determining the on/ off status of generating units that minimize the operating cost during a given time horizon. Since various system and generation constraints are to be satisfied while finding the optimum schedule, UCP turns to be a constrained optimization problem in power system scheduling. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision making task and an efficient Reinforcement Learning solution is formulated considering minimum up time /down time constraints. The correctness and efficiency of the developed solutions are verified for standard test systems

Reinforcement Learning solution for Unit Commitment Problem through pursuit method

Unit commitment is an optimization task in electric power generation control sector. It involves scheduling the ON/OFF status of the generating units to meet the load demand with minimum generation cost satisfying the different constraints existing in the system. Numerical solutions developed are limited for small systems and heuristic methodologies find difficulty in handling stochastic cost functions associated with practical systems. This paper models Unit Commitment as a multi stage decision task and Reinforcement Learning solution is formulated through one efficient exploration strategy: Pursuit method. The correctness and efficiency of the developed solutions are verified for standard test systems

Spatial Variability and Contamination of Heavy Metals in the Inter-tidal Systems of a Tropical Environment

Heavy metals in the surface sediments of the two coastal ecosystems of Cochin, southwest India were assessed. The study intends to evaluate the degree of anthropogenic influence on heavy metal concentration in the sediments of the mangrove and adjacent estuarine stations using enrichment factor and geoaccumulation index. The inverse relationship of Cd and Zn with texture in the mangrove sediments suggested the anthropogenic enrichment of these metals in the mangrove systems. In the estuarine sediments, the absence of any significant correlation of the heavy metals with other sedimentary parameters and their strong interdependence revealed the possibility that the input is not through the natural weathering processes. The analysis of enrichment factor indicated a minor enrichment for Pb and Zn in mangrove sediments. While, extremely severe enrichment for Cd, moderate enrichment for Zn and minor enrichment of Pb were observed in estuarine system. The geo accumulation index exhibited very low values for all metals except Zn, indicating the sediments of the mangrove ecosystem are unpolluted to moderately polluted by anthropogenic activities. However, very strongly polluted condition for Cd and a moderately polluted condition for Zn were evident in estuarine sediments

Sustainable Solid Waste Management Through Ecological Footprint Analysis – A Solution To Kochi City, India

Kochi, the commercial capital of Kerala, South India and second most important city next to Mumbai on the Western coast is a land having a wide variety of residential environments. Due to rapid population growth, changing lifestyles, food habits and living standards, institutional weaknesses, improper choice of technology and public apathy, the present pattern of the city can be classified as that of haphazard growth with typical problems characteristics of unplanned urban development especially in the case of solid waste management. To have a better living condition for us and our future generations, we must know where we are now and how far we need to go. We, each individual must calculate how much nature we use and compare it to how much nature we have available. This can be achieved by applying the concept of ecological footprint. Ecological footprint analysis (EFA) is a quantitative tool that represents the ecological load imposed on earth by humans in spatial terms. The aim of applying EFA to Kochi city is to quantify the consumption and waste generation of a population and to compare it with the existing biocapacity. By quantifying the ecological footprint we can formulate strategies to reduce the footprint and there by having a sustainable living. The paper discusses the various footprint components of Kochi city and in detail analyses the waste footprint of the residential areas using waste footprint analyzer. An attempt is also made to suggest some waste foot print reduction strategies thereby making the city sustainable as far as solid waste management is concerned.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Relativistische vier und zwei Spinor Finite Elemente Berechnungen zweiatomiger Moleküle

Der Vielelektronen Aspekt wird in einteilchenartigen Formulierungen berücksichtigt, entweder in Hartree-Fock Näherung oder unter dem Einschluß der Elektron-Elektron Korrelationen durch die Dichtefunktional Theorie. Da die Physik elektronischer Systeme (Atome, Moleküle, Cluster, Kondensierte Materie, Plasmen) relativistisch ist, habe ich von Anfang an die relativistische 4 Spinor Dirac Theorie eingesetzt, in jüngster Zeit aber, und das wird der hauptfortschritt in den relativistischen Beschreibung durch meine Promotionsarbeit werden, eine ebenfalls voll relativistische, auf dem sogenannten Minimax Prinzip beruhende 2-Spinor Theorie umgesetzt. Im folgenden ist eine kurze Beschreibung meiner Dissertation: Ein wesentlicher Effizienzgewinn in der relativistischen 4-Spinor Dirac Rechnungen konnte durch neuartige singuläre Koordinatentransformationen erreicht werden, so daß sich auch noch für das superschwere Th2 179+ hächste Lösungsgenauigkeiten mit moderatem Computer Aufwand ergaben, und zu zwei weiteren interessanten Veröffentlichungen führten (Publikationsliste). Trotz der damit bereits ermöglichten sehr viel effizienteren relativistischen Berechnung von Molekülen und Clustern blieben diese Rechnungen Größenordnungen aufwendiger als entsprechende nicht-relativistische. Diese behandeln das tatsächliche (relativitische) Verhalten elektronischer Systeme nur näherungsweise richtig, um so besser jedoch, je leichter die beteiligten Atome sind (kleine Kernladungszahl Z). Deshalb habe ich nach einem neuen Formalismus gesucht, der dem möglichst gut Rechnung trägt und trotzdem die Physik richtig relativistisch beschreibt. Dies gelingt durch ein 2-Spinor basierendes Minimax Prinzip: Systeme mit leichten Atomen sind voll relativistisch nunmehr nahezu ähnlich effizient beschrieben wie nicht-relativistisch, was natürlich große Hoffnungen für genaue (d.h. relativistische) Berechnungen weckt. Es ergab sich eine erste grundlegende Veröffentlichung (Publikationsliste). Die Genauigkeit in stark relativistischen Systemen wie Th2 179+ ist ähnlich oder leicht besser als in 4-Spinor Dirac-Formulierung. Die Vorteile der neuen Formulierung gehen aber entscheidend weiter: A. Die neue Minimax Formulierung der Dirac-Gl. ist frei von spuriosen Zuständen und hat keine positronischen Kontaminationen. B. Der Aufwand ist weit reduziert, da nur ein 1/3 der Matrix Elemente gegenüber 4-Spinor noch zu berechnen ist, und alle Matrixdimensionen Faktor 2 kleiner sind. C. Numerisch verhält sich die neue Formulierung ähnlilch gut wie die nichtrelativistische Schrödinger Gleichung (Obwohl es eine exakte Formulierung und keine Näherung der Dirac-Gl. ist), und hat damit bessere Konvergenzeigenschaften als 4-Spinor. Insbesondere die Fehlerwichtung (singulärer und glatter Anteil) ist in 2-Spinor anders, und diese zeigt die guten Extrapolationseigenschaften wie bei der nichtrelativistischen Schrödinger Gleichung. Die Ausweitung des Anwendungsbereichs von (relativistischen) 2-Spinor ist bereits in FEM Dirac-Fock-Slater, mit zwei Beispielen CO und N2, erfolgreich gemacht. Weitere Erweiterungen sind nahezu möglich. Siehe Minmax LCAO Nährung.

Solution properties of the de Branges differential recurrence equation

In this 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums thas was published by Askey and Gasper in 1976. The de Branges functions Tn/k(t) are defined as the solutions of a system of differential recurrence equations with suitably given initial values. The essential fact used in the proof of the Bieberbach and Milin conjectures is the statement Tn/k(t)<=0. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system Λn/k(t) which (by Todorov and Wilf) was realized to be directly connected with de Branges', Tn/k(t)=-kΛn/k(t), and the positivity results in both proofs Tn/k(t)<=0 are essentially the same. In this paper we study differential recurrence equations equivalent to de Branges' original ones and show that many solutions of these differential recurrence equations don't change sign so that the above inequality is not as surprising as expected. Furthermore, we present a multiparameterized hypergeometric family of solutions of the de Branges differential recurrence equations showing that solutions are not rare at all.

A semi-phenomenological approach to the structure and transport properties of macromolecules in solution

Motiviert durch die Lebenswissenschaften (Life sciences) haben sich Untersuchungen zur Dynamik von Makromolekülen in Lösungen in den vergangenen Jahren zu einem zukunftsweisenden Forschungsgebiet etabliert, dessen Anwendungen von der Biophysik über die physikalische Chemie bis hin zu den Materialwissenschaften reichen. Neben zahlreichen experimentellen Forschungsprogrammen zur räumlichen Struktur und den Transporteigenschaften grosser MolekÄule, wie sie heute praktisch an allen (Synchrotron-) Strahlungsquellen und den Laboren der Biophysik anzutreffen sind, werden gegenwärtig daher auch umfangreiche theoretische Anstrengungen unternommen, um das Diffusionsverhalten von Makromolekülen besser zu erklären. Um neue Wege für eine quantitative Vorhersagen des Translations- und Rotationsverhaltens grosser Moleküle zu erkunden, wurde in dieser Arbeit ein semiphänomenologischer Ansatz verfolgt. Dieser Ansatz erlaubte es, ausgehend von der Hamiltonschen Mechanik des Gesamtsystems 'Molekül + Lösung', eine Mastergleichung für die Phasenraumdichte der Makromoleküle herzuleiten, die den Einfluss der Lösung mittels effektiver Reibungstensoren erfasst. Im Rahmen dieses Ansatzes gelingt es z.B. (i) sowohl den Einfluss der Wechselwirkung zwischen den makromolekularen Gruppen (den sogenannten molekularen beads) und den Lösungsteilchen zu analysieren als auch (ii) die Diffusionseigen schaften für veschiedene thermodynamische Umgebungen zu untersuchen. Ferner gelang es auf der Basis dieser Näherung, die Rotationsbewegung von grossen Molekülen zu beschreiben, die einseitig auf einer Oberfläche festgeheftet sind. Im Vergleich zu den aufwendigen molekulardynamischen (MD) Simulationen grosser Moleküle zeichnet sich die hier dargestellte Methode vor allem durch ihren hohen `Effizienzgewinn' aus, der für komplexe Systeme leicht mehr als fünf Grössenordnungen betragen kann. Dieser Gewinn an Rechenzeit erlaubt bspw. Anwendungen, wie sie mit MD Simulationen wohl auch zukünftig nicht oder nur sehr zögerlich aufgegriffen werden können. Denkbare Anwendungsgebiete dieser Näherung betreffen dabei nicht nur dichte Lösungen, in denen auch die Wechselwirkungen der molekularen beads zu benachbarten Makromolekülen eine Rolle spielt, sondern auch Untersuchungen zu ionischen Flüssigkeiten oder zur Topologie grosser Moleküle.

Solution of the Hartree-Fock equations for atoms and diatomic molecules with the finite element method

The finite element method (FEM) is now developed to solve two-dimensional Hartree-Fock (HF) equations for atoms and diatomic molecules. The method and its implementation is described and results are presented for the atoms Be, Ne and Ar as well as the diatomic molecules LiH, BH, N_2 and CO as examples. Total energies and eigenvalues calculated with the FEM on the HF-level are compared with results obtained with the numerical standard methods used for the solution of the one dimensional HF equations for atoms and for diatomic molecules with the traditional LCAO quantum chemical methods and the newly developed finite difference method on the HF-level. In general the accuracy increases from the LCAO - to the finite difference - to the finite element method.

Finite element method for the accurate solution of diatomic molecules

We present the Finite-Element-Method (FEM) in its application to quantum mechanical problems solving for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations of molecules like N_2 and C0 have been obtained. The accuracy achieved with less then 5000 grid points for the total energies of these systems is 10_-8 a.u., which is demonstrated for N_2.

Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations for molecules like N_2 and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is 10^-8 a.u., which is about two orders of magnitude better than the accuracy of any other available method.

Ions of the superheavy elements in vacuum and in solution

The extension of the Periodic Table into the range of unknown atomic numbers of above one hundred requires relativistic calculations. The results of the latter are used to indicate probable values for X-ray transition lines which will be useful for identification of the atomic species formed during collision between accelerated ions and the target. If the half-lives of the isotopes are long, then the chemistry of these new species becomes an important question which is reviewed for E110, E 111 and E112. The possible structural chemistry of the elements E108 to E112 is suggested. Finally the effects of solvation on ions of the actinide and superheavy elements have been studied.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

Constructing a ‘moment of crisis’ and its adequate solution

The rejection of the European Constitution marks an important crystallization point for debate about the European Union (EU) and the integration process. The European Constitution was envisaged as the founding document of a renewed and enlarged European Union and thus it was rather assumed to find wide public support. Its rejection was not anticipated. The negative referenda in France and the Netherlands therefore led to a controversial debate about the more fundamental meaning and the consequences of the rejection both for the immediate state of affairs as well as for the further integration process. The rejection of the Constitution and the controversy about its correct interpretation therefore present an intriguing puzzle for political analysis. Although the treaty rejection was taken up widely in the field of European Studies, the focus of existing analyses has predominantly been on explaining why the current situation occurred. Underlying these approaches is the premise that by establishing the reasons for the rejection it is possible to derive the ‘true’ meaning of the event for the EU integration process. In my paper I rely on an alternative, discourse theoretical approach which aims to overcome the positivist perspective dominating the existing analyses. I argue that the meaning of the event ‘treaty rejection’ is not fixed or inherent to it but discursively constructed. The critical assessment of this concrete meaning-production is of high relevance as the specific meaning attributed to the treaty rejection effectively constrains the scope for supposedly ‘reasonable’ options for action, both in the concrete situation and in the further European integration process more generally. I will argue that the overall framing suggests a fundamental technocratic approach to governance from part of the Commission. Political struggle and public deliberation is no longer foreseen as the concrete solutions to the citizens’ general concerns are designed by supposedly apolitical experts. Through the communicative diffusion and the active implementation of this particular model of governance the Commission shapes the future integration process in a more substantial way than is obvious from its seemingly limited immediate problem-solving orientation of overcoming the ‘constitutional crisis’. As the European Commission is a central actor in the discourse production my analysis focuses on the specific interpretation of the situation put forward by the Commission. In order to work out the Commission’s particular take on the event I conducted a frame analysis (according to Benford/Snow) on a body of key sources produced in the context of coping with the treaty rejection.

On Solution Sets of Information Inequalities

We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce important properties of Bayesian networks, which is important within causal inference.