Identification of heat exchange process in the evaporators of absorption refrigerating units under conditions of uncertainty

Проведено аналіз функціонування випарників абсорбційно-холодильних установок блоку вторинної конденсації типового для України агрегату синтезу аміаку. Обґрунтована необхідність мінімізації температури вторинної конденсації за рахунок створення автоматизованої адаптивної системи оптимального програмного управління. Встановлені рівняння для чисельної оцінки невизначеності теплового навантаження випарника та коефіцієнту теплопередачі. Розроблено алгоритмічне забезпечення щодо розв’язання задач ідентифікації та створення математичної моделі. Визначена технічна структура автоматизованої системи для їх реалізації

Self-stabilizing uncoupled dynamics

Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players' preferences. Recognizing an equilibrium in this setting is a distributed computational task. Self-stabilizing uncoupled dynamics, then, have both resilience to arbitrary initial states and distribution of knowledge. We study these dynamics by analyzing their behavior in a bounded-recall synchronous environment. We determine, for every "size" of game, the minimum number of periods of play that stochastic (randomized) players must recall in order for uncoupled dynamics to be self-stabilizing. We also do this for the special case when the game is guaranteed to have unique best replies. For deterministic players, we demonstrate two self-stabilizing uncoupled protocols. One applies to all games and uses three steps of recall. The other uses two steps of recall and applies to games where each player has at least four available actions. For uncoupled deterministic players, we prove that a single step of recall is insufficient to achieve self-stabilization, regardless of the number of available actions

Algorithmic tools for optimizing the temperature regime of evaporator at absorption refrigeration units of ammonia production

Проведено аналіз випарників абсорбційно-холодильних установок блоку вторинної конденсації виробництва аміаку як об’єктів керування. Визначені координати векторів стану, керування та зовнішніх збурень. Обґрунтована необхідність розв'язання задачi мiнiмiзацiї температури охолодження циркуляційного газу у випарниках для пiдвищення енергоефективностi виробництва. За результатами аналізу промислового апаратурно-технологічного оформлення блоків первинної i вторинної конденсації з'ясовані особливостi умов роботи випарника, що зумовлюють параметричну невизначенiсть у функцiонуваннi об’єктiв керування. Основна з таких невизначеностей пов’язана з керуючою дією витрати флегми. Методом математичного моделювання за розробленим алгоритмом визначені закономiрностi керуючої дiї витрати флегми на ефективнiсть процесiв теплообміну у випарниках абсорбцiйно холодильних установок. Встановлено екстремальний характер залежностi тепловогопотоку (холодопродуктивностi) та температури охолодження циркуляцiйного газу вiд витрати флегми. Максимальна холодопродуктивнiсть, а отже i мiнiмальна температура охолодження циркуляцiйного газу за певного температурного напору, обумовленi досягненням критичного режиму бульбашкового кипiння холодоагенту. Подальше збiльшення температурного напору з пiдвищенням витрати флегми сприяє встановленню перехiдного режиму i зниженню ефективностi поверхнi теплообмiну. Визначенi показники енергоефективностi виробництва амiаку, а саме витрати природного газу в умовах змiни керуючої дiї витрати флегми та значень координат вектора збурень. Розроблене алгоритмiчне забезпечення дозволяє здiйснити розв’язання задачi мiнiмiзацiї температури охолодження циркуляцiйного газу безградiєнтним способом крокового типу з використанням методiв одномiрного пошуку екстремуму. Показано, що за рахунок мiнiмiзацiї температури охолодження циркуляцiйного газу рiчна витрата природного газу може бути знижена в середньому на 500 тис. нм3

Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries

Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point by querying it. The learning objective is to know, for any point in the simplex, a label that occurs within some distance $\epsilon$ from that point. We present two algorithms for this task: Constant-Dimension Generalised Binary Search (CD-GBS), which for constant $m$ uses $poly(n, \log \left( \frac{1}{\epsilon} \right))$ queries, and Constant-Region Generalised Binary Search (CR-GBS), which uses CD-GBS as a subroutine and for constant $n$ uses $poly(m, \log \left( \frac{1}{\epsilon} \right))$ queries. We show via Kakutani's fixed-point theorem that these algorithms provide bounds on the best-response query complexity of computing approximate well-supported equilibria of bimatrix games in which one of the players has a constant number of pure strategies. We also partially extend our results to games with multiple players, establishing further query complexity bounds for computing approximate well-supported equilibria in this setting.Comment: 38 pages, 7 figures, second version strengthens lower bound in Theorem 6, adds footnotes with additional comments and fixes typo

Query Complexity of Approximate Equilibria in Anonymous Games

We study the computation of equilibria of anonymous games, via algorithms that may proceed via a sequence of adaptive queries to the game's payoff function, assumed to be unknown initially. The general topic we consider is \emph{query complexity}, that is, how many queries are necessary or sufficient to compute an exact or approximate Nash equilibrium. We show that exact equilibria cannot be found via query-efficient algorithms. We also give an example of a 2-strategy, 3-player anonymous game that does not have any exact Nash equilibrium in rational numbers. However, more positive query-complexity bounds are attainable if either further symmetries of the utility functions are assumed or we focus on approximate equilibria. We investigate four sub-classes of anonymous games previously considered by \cite{bfh09, dp14}. Our main result is a new randomized query-efficient algorithm that finds a $O(n^{-1/4})$-approximate Nash equilibrium querying $\tilde{O}(n^{3/2})$ payoffs and runs in time $\tilde{O}(n^{3/2})$. This improves on the running time of pre-existing algorithms for approximate equilibria of anonymous games, and is the first one to obtain an inverse polynomial approximation in poly-time. We also show how this can be utilized as an efficient polynomial-time approximation scheme (PTAS). Furthermore, we prove that $\Omega(n \log{n})$ payoffs must be queried in order to find any $\epsilon$-well-supported Nash equilibrium, even by randomized algorithms

Finite Size Effect on Correlation Functions of a Bose Gas in a Trap and Destruction of the Order Parameter by Phase Fluctuations

The influence of the finite sizes on the coherent properties of 3D Bose systems is considered. As is shown, the correlation functions of a Bose gas in a trap have essential differences from analogous correlation functions in an infinite system. Thus, the anomalous correlation function vanishes due to the divergency of phase fluctuations which destruct the order parameter too. The normal correlation function decays exponentially in time for sufficiently large time interval.Comment: 10 pages, RevTex4, some references have been added some changes in text are mad

Magnetic-field-induced Luttinger liquid

It is shown that a strong magnetic field applied to a bulk metal induces a Luttinger-liquid phase. This phase is characterized by the zero-bias anomaly in tunneling: the tunneling conductance scales as a power-law of voltage or temperature. The tunneling exponent increases with the magnetic field as BlnB. The zero-bias anomaly is most pronounced for tunneling with the field applied perpendicular to the plane of the tunneling junction.Comment: a reference added, minor typos correcte

S-matrix for magnons in the D1-D5 system

We show that integrability and symmetries of the near horizon geometry of the D1-D5 system determine the S-matrix for the scattering of magnons with polarizations in AdS3 $\times$ S3 completely up to a phase. Using semi-classical methods we evaluate the phase to the leading and to the one-loop approximation in the strong coupling expansion. We then show that the phase obeys the unitarity constraint implied by the crossing relations to the one-loop order. We also verify that the dispersion relation obeyed by these magnons is one-loop exact at strong coupling which is consistent with their BPS nature.Comment: 40 pages, Latex, Role of Virasoro constraints clarified, version matches with published versio

Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux

We study superstrings on AdS_3 x S^3 x T^4 supported by a combination of Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz three form fluxes, and construct a set of finite-gap equations that describe the classical string spectrum. Using the recently proposed all-loop S-matrix we write down the all-loop Bethe ansatz equations for the massive sector. In the thermodynamic limit the Bethe ansatz reproduces the finite-gap equations. As part of this derivation we propose expressions for the leading order dressing phases. These phases differ from the well-known Arutyunov-Frolov-Staudacher phase that appears in the pure Ramond-Ramond case. We also consider the one-loop quantization of the algebraic curve and determine the one-loop corrections to the dressing phases. Finally we consider some classical string solutions including finite size giant magnons and circular strings.Comment: 44 pages, 3 figures. v2: references and a discussion about perturbative results adde

Do attractive bosons condense?

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. ^7Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a `fragmented' condensate discussed by Nozi\`eres and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.Comment: 4 pages, Latex, RevTe