On examples of difference operators for {0,1}\{0,1\}-valued functions over finite sets

Recently V.I.Arnold have formulated a geometrical concept of monads and apply it to the study of difference operators on the sets of $\{0,1\}$-valued sequences of length $n$. In the present note we show particular examples of these monads and indicate one question arising here

Lie Groups and mechanics: an introduction

The aim of this paper is to present aspects of the use of Lie groups in mechanics. We start with the motion of the rigid body for which the main concepts are extracted. In a second part, we extend the theory for an arbitrary Lie group and in a third section we apply these methods for the diffeomorphism group of the circle with two particular examples: the Burger equation and the Camassa-Holm equation

Skylux Smartphone Controlled Skylight

There are numerous electric skylight openers available for purchase for home-use, but the majority of them are remote based, or operated by a wall-unit. Furthermore, these devices are in hard to reach places, so if one were to lose the remote on a remote operated system, the only option is to contact the manufacturer for a new device. As such, my senior project, in collaboration with Colton Sundstrom’s senior project, build upon our existing capstone project in order to allow operation of the Internet of Things (IoT) device over the internet. Our client, Richard Murray, was unsatisfied with the current state of his Velux skylight operator, so we wanted to create an end-product that could allow the operation to be controllable with any of his iOS devices, whether or not he was at home. Furthermore, the end-product should be secure, in that only authorized users could control the device. Since my client deemed that this project is very expansive, this project will also include a setup guide for new students to get the system running on their own environment for further improvements in areas such as scheduling, security, and more expansive features

Observation of a red-blue detuning asymmetry in matter-wave superradiance

We report the first experimental observations of strong suppression of matter-wave superradiance using blue-detuned pump light and demonstrate a pump-laser detuning asymmetry in the collective atomic recoil motion. In contrast to all previous theoretical frameworks, which predict that the process should be symmetric with respect to the sign of the pump-laser detuning, we find that for condensates the symmetry is broken. With high condensate densities and red-detuned light, the familiar distinctive multi-order, matter-wave scattering pattern is clearly visible, whereas with blue-detuned light superradiance is strongly suppressed. In the limit of a dilute atomic gas, however, symmetry is restored.Comment: Accepted by Phys. Rev. Let

Differentiability of solutions of stationary Fokker–Planck–Kolmogorov equations with respect to a parameter

We obtain sufficient conditions for the differentiability of solutions to stationary Fokker-Planck-Kolmogorov equations with respect to a parameter. In particular, this gives conditions for the differentiability of stationary distributions of diffusion processes with respect to a parameter

Single-shot discrimination of quantum unitary processes

We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a "fidelity-like" lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of apriori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimization of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur

Theoretical Aspects of Creating the Business Models for Supply Chain Process of Industrial Enterprises

Abstract- Creating the business models for supply chain process is the subject of modern scientific research in the field of strategic planning and management of the enterprise. Some theoretical and practical aspects have not yet received a comprehensive scientific substantiation. General problem of enterprise management is traditionally analyzed in the researches, and business modeling is not fully investigated. The current state of the economy and peculiarities of its development, as well as the transformational nature of the Russian economy, show that the most important theoretical and practical aspects, which require scientific attention and development, analysis and systematization, are the theoretical provisions of business modeling concept for supply chain process; clarification of the term "business model" for supply chain process of an industrial enterprise; definition of the main elements and substantiation of the technology of business model formation; systematization and generalization of modern methods of strategic analysis; formation of an integrated system for assessment the effectiveness of the enterprises business model for supply chain process. The issues of strategic development of the enterprise always arouse a great interest among researchers. Today, a significant number of business models have been created for the development of enterprises of various industry structures. The purpose of the article is to systematize the information about the creation of business models for supply chain process of industrial enterprises, to consider the features of the models use at the present stage. Scientific and theoretical basis of the research was the methods of analysis and synthesis, scientific abstraction, the use of quantitative and qualitative assessment methods, with the help of which the categories of the concept business model for the supply chain process were defined. Endogenous and exogenous factors, influencing the functioning of enterprises business models were identified. The article deals with the conceptual issues of the business model for the supply chain process formation, in particular, the essence and peculiarities of modern business models, as well as management approaches to the processes of development of enterprises business model for supply chain process. Keywords: business model, strategic development, industrial enterprise, supply chain process, creation

Classical Signal Model for Quantum Channels

Recently it was shown that the main distinguishing features of quantum mechanics (QM) can be reproduced by a model based on classical random fields, so called prequantum classical statistical field theory (PCSFT). This model provides a possibility to represent averages of quantum observables, including correlations of observables on subsystems of a composite system (e.g., entangled systems), as averages with respect to fluctuations of classical (Gaussian) random fields. In this note we consider some consequences of PCSFT for quantum information theory. They are based on the observation \cite{W} of two authors of this paper that classical Gaussian channels (important in classical signal theory) can be represented as quantum channels. Now we show that quantum channels can be represented as classical linear transformations of classical Gaussian signa

Pattern of Midface Trauma with Associated Concomitant Injuries in a Nigerian Referral Centre

Aim: The aim of this study was to determine the pattern of midface trauma with associated concomitant injuries seen in our environment. Methodology: This was a prospective analysis of trauma patients with midfacial injuries presenting at a referral center in South West Nigeria. In addition to socio‑demographic data, the following information was also obtained: Mechanism of injuries, type of midfacial injuries, concomitant/associated injuries and treatment. Results: A total of 101 patients with midfacial injuries were involved. They were made up of 85 males and 16 females. The 20‑29 year age group was mostly affected (44.6%) and the most common cause of midface injuries was road traffic accident (91.1%). The zygoma was fractured more than any other midfacial bone (46.0%). A total of 144 associated injuries were recorded among these patients, head and ocular injuries accounted for 49 (34%) and 35 (24.3%) respectively. The patients were mostly treated conservatively or by closed reduction. Conclusion: The rate of head and ocular injuries among patients with midfacial injury was high. Knowledge of these associated injuries provides useful strategies for patient care and prevention of further complications. A multidisciplinary approach is important for optimum management of these patients.Keywords: Concomitant injuries, midface trauma, multidisciplinary car