2,886 research outputs found
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
and exact solutions are also constructed for reaction orders . 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
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