Multiplier Sequences for Simple Sets of Polynomials

In this paper we give a new characterization of simple sets of polynomials B with the property that the set of B-multiplier sequences contains all Q-multiplier sequence for every simple set Q. We characterize sequences of real numbers which are multiplier sequences for every simple set Q, and obtain some results toward the partitioning of the set of classical multiplier sequences

Persistence of transition state structure in chemical reactions driven by fields oscillating in time

Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving, barrier top also fails to be recrossing-free. We construct a moving dividing surface in phase space over a transition state trajectory. This surface is recrossing-free for both Hamiltonian and dissipative dynamics. This is confirmed even for strongly anharmonic barriers using simulation. The power of transition state theory is thereby applicable to chemical reactions and other activated processes even when the bottlenecks are time-dependent and move across space

Chemical reactions induced by oscillating external fields in weak thermal environments

Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally varying external field, the transition state that the reaction must pass through during the transformation from reactant to product is no longer a fixed geometric structure, but is instead time-dependent. For a periodically forced model reaction, we develop a recrossing-free dividing surface that is attached to a transition state trajectory [T. Bartsch, R. Hernandez, and T. Uzer, Phys. Rev. Lett. 95, 058301 (2005)]. We have previously shown that for single-mode sinusoidal driving, the stability of the time-varying transition state directly determines the reaction rate [G. T. Craven, T. Bartsch, and R. Hernandez, J. Chem. Phys. 141, 041106 (2014)]. Here, we extend our previous work to the case of multi-mode driving waveforms. Excellent agreement is observed between the rates predicted by stability analysis and rates obtained through numerical calculation of the reactive flux. We also show that the optimal dividing surface and the resulting reaction rate for a reactive system driven by weak thermal noise can be approximated well using the transition state geometry of the underlying deterministic system. This agreement persists as long as the thermal driving strength is less than the order of that of the periodic driving. The power of this result is its simplicity. The surprising accuracy of the time-dependent noise-free geometry for obtaining transition state theory rates in chemical reactions driven by periodic fields reveals the dynamics without requiring the cost of brute-force calculations

A New Class of Non-Linear Stability Preserving Operators

We extend Br\"and\'en's recent proof of a conjecture of Stanley and describe a new class of non-linear operators that preserve weak Hurwitz stability and the Laguerre-P\'olya class.Comment: Fixed typos, spelling, and updated links in reference

A systematic review and meta-analysis of the criterion validity of nutrition assessment tools for diagnosing protein-energy malnutrition in the older community setting

Background: Accurate diagnosis is a key step in managing protein-energy malnutrition. This review seeks to determine the criterion (concurrent and predictive) validity and reliability of nutrition assessment tools in making a diagnosis of protein-energy malnutrition in community-living older adults. Methods: A systematic literature review was undertaken using six electronic databases in September 2016. Studies in any language were included which measured malnutrition via a nutrition assessment tool in adults ≥65 years living in their own homes. Data relating to the predictive validity of tools were analysed via meta-analyses. GRADE was used to evaluate the body of evidence. Results: There were 6,412 records identified, of which eight papers were included. Two studies evaluated the concurrent validity of the Mini Nutritional Assessment (MNA) and Subjective Global Assessment (SGA) and six evaluated the predictive validity of the MNA. The quality of the body of evidence for the concurrent validity of both the MNA andSGA was very low. The quality of the body of evidence for the predictive validity of the MNA in detecting risk of death was moderate (RR: 1.92 [95%CI: 1.55-2.39]; P Conclusions: Due to the small number of studies identified and no evaluation of the predictive validity of tools other than the MNA, there is insufficient evidence to recommend a particular nutrition assessment tool for diagnosing protein-energy malnutrition in older adults in the community setting. High quality diagnostic accuracy studies are needed for all nutrition assessment tools used in older community samples, including measuring of health outcomes subsequent to nutrition assessment by the SGA and PG-SGA

A systematic review and meta-analysis of the criterion validity of nutrition assessment tools for diagnosing protein-energy malnutrition in the older community setting (the MACRo Study)

Background & aims: Malnutrition is a significant barrier to healthy and independent ageing in older adults who live in their own homes, and accurate diagnosis is a key step in managing the condition. However, there has not been sufficient systematic review or pooling of existing data regarding malnutrition diagnosis in the geriatric community setting. The current paper was conducted as part of the MACRo (Malnutrition in the Ageing Community Review) Study and seeks to determine the criterion (concurrent and predictive) validity and reliability of nutrition assessment tools in making a diagnosis of protein-energy malnutrition in the general older adult community. Methods: A systematic literature review was undertaken using six electronic databases in September 2016. Studies in any language were included which measured malnutrition via a nutrition assessment tool in adults ≥65 years living in their own homes. Data relating to the predictive validity of tools were analysed via meta-analyses. GRADE was used to evaluate the body of evidence. Results: There were 6412 records identified, of which 104 potentially eligible records were screened via full text. Eight papers were included; two which evaluated the concurrent validity of the Mini Nutritional Assessment (MNA) and Subjective Global Assessment (SGA) and six which evaluated the predictive validity of the MNA. The quality of the body of evidence for the concurrent validity of both the MNA and SGA was very low. The quality of the body of evidence for the predictive validity of the MNA in detecting risk of death was moderate (RR: 1.92 [95% CI: 1.55–2.39]; P < 0.00001; n = 2013 participants; n = 4 studies; I2: 0%). The quality of the body of evidence for the predictive validity of the MNA in detecting risk of poor physical function was very low (SMD: 1.02 [95%CI: 0.24–1.80]; P = 0.01; n = 4046 participants; n = 3 studies; I2:89%). Conclusions: Due to the small number of studies identified and no evaluation of the predictive validity of tools other than the MNA, there is insufficient evidence to recommend a particular nutrition assessment tool for diagnosing PEM in older adults in the community. High quality diagnostic accuracy studies are needed for all nutrition assessment tools used in older community samples, including measuring of health outcomes subsequent to nutrition assessment by the SGA and PG-SGA

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders $n \in \mathbb{R}_{>0}$ and exact solutions are also constructed for reaction orders $n \in \mathbb{N}: n \leq 3$. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically