Logic hybrid simulation-optimization algorithm for distillation design

In this paper, we propose a novel algorithm for the rigorous design of distillation columns that integrates a process simulator in a generalized disjunctive programming formulation. The optimal distillation column, or column sequence, is obtained by selecting, for each column section, among a set of column sections with different number of theoretical trays. The selection of thermodynamic models, properties estimation etc., are all in the simulation environment. All the numerical issues related to the convergence of distillation columns (or column sections) are also maintained in the simulation environment. The model is formulated as a Generalized Disjunctive Programming (GDP) problem and solved using the logic based outer approximation algorithm without MINLP reformulation. Some examples involving from a single column to thermally coupled sequence or extractive distillation shows the performance of the new algorithm.

Truth Values in t-norm based Systems Many-valued FUZZY Logic

In t-norm based systems many-valued logic, valuations of propositions form a non-countable set: interval [0,1]. In addition, we are given a set E of truth values p, subject to certain conditions, the valuation v is v=V(p), V reciprocal application of E on [0,1]. The general propositional algebra of t-norm based many-valued logic is then constructed from seven axioms. It contains classical logic (not many-valued) as a special case. It is first applied to the case where E=[0,1] and V is the identity. The result is a t-norm based many-valued logic in which contradiction can have a nonzero degree of truth but cannot be true; for this reason, this logic is called quasi-paraconsistent.

Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers

Paraconsistent logic admits that the contradiction can be true. Let p be the truth values and P be a proposition. In paraconsistent logic the truth values of contradiction is . This equation has no real roots but admits complex roots . This is the result which leads to develop a multivalued logic to complex truth values. The sum of truth values being isomorphic to the vector of the plane, it is natural to relate the function V to the metric of the vector space R2. We will adopt as valuations the norms of vectors. The main objective of this paper is to establish a theory of truth-value evaluation for paraconsistent logics with the goal of using in analyzing ideological, mythical, religious and mystic belief systems.

Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Profitability analysis of a femtosecond laser system for cataract surgery using a fuzzy logic approach

AIM: To define the financial and management conditions required to introduce a femtosecond laser system for cataract surgery in a clinic using a fuzzy logic approach. METHODS: In the simulation performed in the current study, the costs associated to the acquisition and use of a commercially available femtosecond laser platform for cataract surgery (VICTUS, TECHNOLAS Perfect Vision GmbH, Bausch & Lomb, Munich, Germany) during a period of 5y were considered. A sensitivity analysis was performed considering such costs and the countable amortization of the system during this 5y period. Furthermore, a fuzzy logic analysis was used to obtain an estimation of the money income associated to each femtosecond laser-assisted cataract surgery (G). RESULTS: According to the sensitivity analysis, the femtosecond laser system under evaluation can be profitable if 1400 cataract surgeries are performed per year and if each surgery can be invoiced more than $500. In contrast, the fuzzy logic analysis confirmed that the patient had to pay more per surgery, between $661.8 and $667.4 per surgery, without considering the cost of the intraocular lens (IOL). CONCLUSION: A profitability of femtosecond laser systems for cataract surgery can be obtained after a detailed financial analysis, especially in those centers with large volumes of patients. The cost of the surgery for patients should be adapted to the real flow of patients with the ability of paying a reasonable range of cost.

The London and Edinburgh philosophical magazine and journal of science.

3rd ser. : v.10 (1837 : Jan.-June)

The Edinburgh new philosophical journal.

v.31 (1841)

The Summary of a Course of Experimental Philosophical Lectures, 1746-1747

Leather hardcover notebook containing a handwritten copy of John Winthrop's course of experimental and philosophical lectures presented between March 10, 1746 and June 16, 1746. The first one-hundred pages of the volume are divided into twenty chapters which were presented in thirty-three lectures. The chapters contain text and diagrams on mechanical powers, the lever, the pulley, the axis in peritrochio, the inclined plane, the wedge, the screw, compound engines, the laws of motion, gravity, attraction of cohesion, the power of repulsion, magnetism, fluids, electricity, opticks, and astronomy. There is a five-page addenda to the course summary added in 1747, and a sixty-page text titled "The Method of Astronomical calculations" containing thirteen problems related to calculating distances with a list of astronomical characters, and followed with charts related to the eclipse of Jupiter's satellites.

From Dr. Watt's Philosophical Essays, undated

Three leaves containing handwritten extracts and notes on sections II and III of Isaac Watt's essay, "A fair inquiry and debate concerning space, whether it be something or nothing, God or Creature." A section of notes for a third essay is incomplete.

Transactions of the American Philosophical Society.

new ser.:v.2 (1825)

Transactions of the American Philosophical Society.

new ser.:v.16 (1890)

Transactions of the American Philosophical Society.

new ser.:v.3 (1830)

Transactions of the American Philosophical Society.

new ser.:v.10 (1853)

List of benefactors who contributed to replacement of books and philosophical apparatus, May 4, 1764

This document lists the names of subscribers who promised funds towards the rebuilding of the library and philosophical apparatus. Entries are divided among three columns, "Apparatus," "Library," and "At large," and include the donor's name and amount promised. Gifts to the library included actual books as well as funds for book purchases.