• U0 = V which is a subspace of R. Thus, U0 is a vector space • Assume that Ui is a vector space, for i ≥ 0. We will show that Ui+1 = Ui ∩A Ui is also a vector space. From the definition of Ui+1, it is clear that Ui+1 ⊆ Ui. We also have: – For any x, y ∈ Ui+1: x, y ∈ Ui ∩ A Ui, thus x ∈ Ui and x ∈ A Ui ⇒ Ax ∈ Ui. Similarly, y ∈ Ui and Ay ∈ Ui. Since Ui is a vector space, it follows that x + y ∈...

INTRODUCTION Ulcerative colitis (UC) require expensive, lifelong treatment, which generates huge direct costs and has a significant impact on the quality of life, especially in the active state of the disease. AIM To assess the indirect costs, health-related quality of life, and clinical characteristics of patients with UC in Poland. Additionally, we investigated the association between activ...

Nowadays, voice assistants help users complete tasks on the smartphone with commands, replacing traditional touchscreen interactions when such are inhibited. However, usability of those tools remains moderate due to problems in understanding rich language variations human along efficiency and comprehensibility issues. Therefore, we introduce Voicify, an Android virtual assistant that allows int...

Introduction UIs are among the leading causes of injury in children younger than 5 years in NYC1. About 3000 calls are received each year by the NYC Poison Control Center (PCC) for this age group1. Common UI exposures include medications, cosmetics, household cleaners, foreign bodies, and pesticides2. We examined UIs in NYC from January 2010 to July 2014 for children <5 years to investigate the...

The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN  of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most      relevant information of X. These eigenvectors are called principal components [8]. Ass...

The enzyme gamma-glutamyltransferase (GGT) is an established marker of liver function and alcohol consumption and represents the major factor responsible for the extra-cellular catabolism of the main antioxidant in mammalian cells, Glutathione. ESRD is a condition characterized by a high risk of death and cardiovascular (CV) complications and with a high prevalence of liver disease but the link...

This paper presents a model predictive control (MPC) of a utility interactive (UI) single phase inverter (SPI) for a photovoltaic (PV) system at residential/distribution level. The proposed model uses single-phase phase locked loop (PLL) to synchronize SPI with the grid and performs MPC control in a dq reference frame. SPI model consists of boost converter (BC), maximum power point tracking (MP...

For some auction, let v1...vn be bidder valuations for bidder i (potentially a vector of valuations, for multiitem auctions). Bidders bid some value bi, such that b = (b1, ...bn). Bidders seek to maximize some utility ui(b, vi), dependent on both the auction outcomes caused by other bids and their own valuation profile. For some distribution over bids N (where b can be sampled from N), this imp...

BACKGROUND AND OBJECTIVE Utilities (values representing preferences) for healthcare priority setting are typically obtained indirectly by asking patients to fill in a quality of life questionnaire and then converting the results to a utility using population values. We compared such utilities with those obtained directly from patients or the public. DESIGN Review of studies providing both a d...