Effect Algebras as Presheaves on Finite Boolean Algebras

For an effect algebra A, we examine the category of all morphisms from finite Boolean algebras into A. This category can be described as a category of elements of a presheaf R(A) on the category of finite Boolean algebras. We prove that some properties (being an orthoalgebra, the Riesz decomposition property, being a Boolean algebra) of an effect algebra A can be characterized in terms of some properties of the category of elements of the presheaf R(A). We prove that the tensor product of effect algebras arises as a left Kan extension of the free product of finite Boolean algebras along the inclusion functor. The tensor product of effect algebras can be expressed by means of the Day convolution of presheaves on finite Boolean algebras.     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

Synchrotron X‐ray footprinting on tour

Synchrotron footprinting is a valuable technique in structural biology for understanding macromolecular solution‐state structure and dynamics of proteins and nucleic acids. Although an extremely powerful tool, there is currently only a single facility in the USA, the X28C beamline at the National Synchrotron Light Source (NSLS), dedicated to providing infrastructure, technology development and support for these studies. The high flux density of the focused white beam and variety of specialized exposure environments available at X28C enables footprinting of highly complex biological systems; however, it is likely that a significant fraction of interesting experiments could be performed at unspecialized facilities. In an effort to investigate the viability of a beamline‐flexible footprinting program, a standard sample was taken on tour around the nation to be exposed at several US synchrotrons. This work describes how a relatively simple and transportable apparatus can allow beamlines at the NSLS, CHESS, APS and ALS to be used for synchrotron footprinting in a general user mode that can provide useful results.     

New precision limit on the strange vector form factors of the proton

The parity-violating cross-section asymmetry in the elastic scattering of polarized electrons from unpolarized protons has been measured at a four-momentum transfer squared Q2 = 0.624 GeV2 and beam energy E(b) = 3.48 GeV to be A(PV) = -23.80 ± 0.78(stat) ± 0.36(syst) parts per million. This result is consistent with zero contribution of strange quarks to the combination of electric and magnetic form factors G(E)(s) + 0.517G(M)(s) = 0.003 ± 0.010(stat) ± 0.004(syst) ± 0.009(ff), where the third error is due to the limits of precision on the electromagnetic form factors and radiative corrections. With this measurement, the world data on strange contributions to nucleon form factors are seen to be consistent with zero and not more than a few percent of the proton form factors.     

Sufficiency in Quantum Statistical Inference

This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means that all information is extracted about the mutual relation of a given family of states. In the paper sufficient coarse-grainings are characterized in several equivalent ways and the non-commutative analogue of the factorization theorem is obtained. As an application we discuss exponential families. Our factorization theorem also implies two further important results, previously known only in finite Hilbert space dimension, but proved here in generality: the Koashi-Imoto theorem on maps leaving a family of states invariant, and the characterization of the general form of states in the equality case of strong subadditivity. Supported by the EU Research Training Network Quantum Probability with Applications to Physics, Information Theory and Biology and Center of Excellence SAS Physics of Information I/2/2005. Supported by the Hungarian grant OTKA T032662     

Simple dose rate measurements for a very high synchrotron X‐ray flux

Dose measurements based on methylene blue (MB) bleaching, widely used for ultraviolet light, can also be applied to X‐rays including very high flux levels. This method has been tested by using both MB bleaching and Fricke dosimetry for a conventional monochromatic X‐ray source and then for `white‐beam' synchrotron radiation. The results show that MB bleaching dosimetry can easily measure X‐ray doses up to at least 10⁵ Gy s^?1, as long as the MB concentration is sufficiently high. This condition can be verified from the deviations from linearity of the bleaching versus exposure time.     

Removal of C3F8 Via the Combination of Non-Thermal Plasma, Adsorption and Catalysis

The feasibility of C₃F₈ abatement via combining nonthermal plasma with adsorption and/or catalysis is investigated in this study. In terms of the simultaneous combination of plasma, adsorption and catalysis (CPAC), three different configurations including A/C layer (adsorbent layer prior to catalyst layer), C/A layer (catalyst layer prior to adsorbent layer) and A/C mixture (adsorbent and catalyst are mechanically mixed) are adopted. For all the experimental tests conducted in this study, the gas stream consists of 500 ppm C₃F₈, 2% O₂, and balanced N₂. The experimental results indicate that C₃F₈ removal efficiencies depend on what kind of packing material is adopted (adsorbent, catalyst or both) and how the material is packed within the plasma reactor. The removal efficiencies obtained with different reactors are in the order as: CPAC (A/C layer; AC mixture) > CPA (plasma with adsorbent alone) > CPC (plasma with catalyst alone) > CPAC (C/A layer). The indentified products after treatment include CO₂, CO, N₂O and CF₄. The formation of C₂F₆ is not observed in this study, which is encouraging since the global warming potential of C₂F₆ is actually higher than that of C₃F₈.     

Transport Polymerization of Gaseous Intermediates and Polymer Crystals Growth

Man is always enchanted with discoveries of new and better ways of making things. Even after more than a hundred years of synthetic chemistry, scientists are today still as enthusiastic as ever looking for “novel” reactions and “novel” syntheses. One of the great achievements of the last decade was the development and usage of “intermediates” for syntheses. Knowing the extensive applications [1-4] of these intermediates in modern synthetic chemistry, it is, however, surprising to find that only few groups of these intermediates have been used in polymer syntheses. For instance [5], even though there are radical polymerizations and polymerizations involving carbanions and carbonium ions, there are practically no polymer syntheses using benzynes [2], carbenes [3], or nitrenes [4].     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part I. Fundamental concepts

A method is proposed that should facilitate the construction of theories of submicroscopic particles (denoted as theories of microchannels) in a way similar to the use of group-theoretical methods. The conceptual analysis (CA) method is based on the analysis of the basic concepts of a theory; it permits a determination of necessary conditions imposed on the mathematical apparatus (of the theory) which then appear as a mathematical representation of the structures obtained in a formal scheme of a theory. A pertinent conceptual analysis leads to a new definition (relativization) of the concept empirical implication. The approach may be characterized as realistic and operational. The application of the CA method is illustrated on the example of quantum theory. In Part I the algebraic structure of a partially ordered, up-ward directed, bounded set is deduced from the rudimentary concepts. In Parts II and III, we shall deduce the Hilbert-space structure (well established in quantum mechanics) from postulates on some essential idealizations accepted in the theory. Whereas Part II is concerned with the idealizations of existing quantum theories based on the Hilbert-space formalism, Part I may be considered as a general basis for a wider class of theories.Dedicated to Prof. G. Ludwig on the occasion of his 60th birthday.