The polymerization of styrene by sulphuric acid - I. Theory of fast-initiated non-stationary polymerization

1961 ◽  
Vol 263 (1312) ◽  
pp. 58-62 ◽  
Keyword(s):  
Sulphuric Acid ◽  
Time Course ◽  
Monomer Concentration ◽  
Degree Of Polymerization ◽  
Average Degree ◽  
Chain Reaction ◽  
First Order ◽  
Chain Lengths ◽  
Special Case ◽  
Termination Process

Theoretical relationships are derived for the time course, yield, and number-average degree of polymerization in a non-stationary chain reaction having a very rapid initiation process and a first-order termination process. The distribution of chain lengths is derived for the special case of constant monomer concentration.

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

scholarly journals Study of the mode of action of a polygalacturonase from the phytopathogen Burkholderia cepacia

2007 ◽  
Vol 407 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Claudia Massa ◽  
Mads H. Clausen ◽  
Jure Stojan ◽  
Doriano Lamba ◽  
Cristiana Campa
Keyword(s):  
Mode Of Action ◽  
Burkholderia Cepacia ◽  
Time Course ◽  
Glycoside Hydrolase Family ◽  
Enzymatic Mechanism ◽  
Processive Enzyme ◽  
Chain Lengths ◽  
Methylation Patterns ◽  
Hydrolysis Of ◽  
Hydrolase Family

We have recently isolated and heterologously expressed BcPeh28A, an endopolygalacturonase from the phytopathogenic Gram-negative bacterium Burkholderia cepacia. Endopolygalacturonases belong to glycoside hydrolase family 28 and are responsible for the hydrolysis of the non-esterified regions of pectins. The mode of action of BcPeh28A on different substrates has been investigated and its enzymatic mechanism elucidated. The hydrolysis of polygalacturonate indicates that BcPeh28A is a non-processive enzyme that releases oligomers with chain lengths ranging from two to eight. By inspection of product progression curves, a kinetic model has been generated and extensively tested. It has been used to derive the kinetic parameters that describe the time course of the formation of six predominant products. Moreover, an investigation of the enzymatic activity on shorter substrates that differ in their overall length and methylation patterns sheds light on the architecture of the BcPeh28A active site. Specifically the tolerance of individual sites towards methylated saccharide units was rationalized on the basis of the hydrolysis of hexagalacturonides with different methylation patterns.

scholarly journals Controlled Depolymerization of Cellulose Fibres Isolated from Lignocellulosic Biomass Wastes

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Suh Cem Pang ◽  
Lee Ken Voon ◽  
Suk Fun Chin
Keyword(s):  
Lignocellulosic Biomass ◽  
Acid Catalyst ◽  
Degree Of Polymerization ◽  
Second Order ◽  
Water Soluble ◽  
Cellulose Fibres ◽  
Amberlyst 15 ◽  
Pseudo Second Order ◽  
Chain Lengths ◽  
Optimized Conditions

Various types of lignocellulosic biomass wastes (LBW) had been successfully converted into cello-oligomers with different chain lengths via a controlled depolymerization process. Cellulose fibres isolated from LBW samples were dissolved with room temperature ionic liquid (RTIL) in the presence of an acid catalyst, Amberlyst 15 DRY. The effects of reaction time on the degree of polymerization and yields of water-insoluble cello-oligomers formed were studied. Besides, the yields of water-soluble cello-oligomers such as glucose and xylose were also determined. The depolymerization of cellulose fibres isolated from LBW was observed to follow both second-order and pseudo-second order kinetics under specific conditions. As such, cello-oligomers of controllable chain lengths could be obtained by adjusting the duration of depolymerization process under optimized conditions.

Uniqueness, definability and interpolation

1988 ◽  
Vol 53 (2) ◽  
pp. 554-570 ◽  
Author(s):  
Kosta Došen ◽  
Peter Schroeder-Heister
Keyword(s):  
Proof Theory ◽  
Interpolation Theorem ◽  
Order Logic ◽  
First Order Logic ◽  
General Notion ◽  
Structural Part ◽  
First Order ◽  
First Case ◽  
Additional Constant ◽  
Special Case

This paper is meant to be a comment on Beth's definability theorem. In it we shall make the following points.Implicit definability as mentioned in Beth's theorem for first-order logic is a special case of a more general notion of uniqueness. If α is a nonlogical constant, Tα a set of sentences, α* an additional constant of the same syntactical category as α and Tα, a copy of Tα with α* instead of α, then for implicit definability of α in Tα one has, in the case of predicate constants, to derive α(x1,…,xn) ↔ α*(x1,…,xn) from Tα ∪ Tα*, and similarly for constants of other syntactical categories. For uniqueness one considers sets of schemata Sα and derivability from instances of Sα ∪ Sα* in the language with both α and α*, thus allowing mixing of α and α* not only in logical axioms and rules, but also in nonlogical assumptions. In the first case, but not necessarily in the second one, explicit definability follows. It is crucial for Beth's theorem that mixing of α and α* is allowed only inside logic, not outside. This topic will be treated in §1.Let the structural part of logic be understood roughly in the sense of Gentzen-style proof theory, i.e. as comprising only those rules which do not specifically involve logical constants. If we restrict mixing of α and α* to the structural part of logic which we shall specify precisely, we obtain a different notion of implicit definability for which we can demonstrate a general definability theorem, where a is not confined to the syntactical categories of nonlogical expressions of first-order logic. This definability theorem is a consequence of an equally general interpolation theorem. This topic will be treated in §§2, 3, and 4.

Combined Implementation of Dynamic Rating-based Protection and Calculating the Average Degree of Polymerization for Power Transformers

2021 ◽  
Vol 141 (7) ◽  
pp. 528-534
Author(s):  
Kohei Ito ◽  
Mutsumi Aoki ◽  
Toru Amau ◽  
Tetsuo Otani ◽  
Tatsuya Ozawa ◽  
...  
Keyword(s):  
Degree Of Polymerization ◽  
Average Degree ◽  
Power Transformers

Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad

2021 ◽  
Author(s):  
Behnam Malakooti ◽  
Mohamed Komaki ◽  
Camelia Al-Najjar
Keyword(s):  
Risk Behaviors ◽  
Empirical Studies ◽  
Dispersion Theory ◽  
Dispersion Models ◽  
Decision Making Under Risk ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Out Of Sample ◽  
Mean Variance ◽  
Special Case

Many studies have spotlighted significant applications of expected utility theory (EUT), cumulative prospect theory (CPT), and mean-variance in assessing risks. We illustrate that these models and their extensions are unable to predict risk behaviors accurately in out-of-sample empirical studies. EUT uses a nonlinear value (utility) function of consequences but is linear in probabilities, which has been criticized as its primary weakness. Although mean-variance is nonlinear in probabilities, it is symmetric, contradicts first-order stochastic dominance, and uses the same standard deviation for both risk aversion and risk proneness. In this paper, we explore a special case of geometric dispersion theory (GDT) that is simultaneously nonlinear in both consequences and probabilities. It complies with first-order stochastic dominance and is asymmetric to represent the mixed risk-averse and risk-prone behaviors of the decision makers. GDT is a triad model that uses expected value, risk-averse dispersion, and risk-prone dispersion. GDT uses only two parameters, z and zX; these constants remain the same regardless of the scale of risk problem. We compare GDT to several other risk dispersion models that are based on EUT and/or mean-variance, and identify verified risk paradoxes that contradict EUT, CPT, and mean-variance but are easily explainable by GDT. We demonstrate that GDT predicts out-of-sample empirical risk behaviors far more accurately than EUT, CPT, mean-variance, and other risk dispersion models. We also discuss the underlying assumptions, meanings, and perspectives of GDT and how it reflects risk relativity and risk triad. This paper covers basic GDT, which is a special case of general GDT of Malakooti [Malakooti (2020) Geometric dispersion theory of decision making under risk: Generalizing EUT, RDEU, & CPT with out-of-sample empirical studies. Working paper, Case Western Reserve University, Cleveland.].

scholarly journals Extraction and Characterization of Inulin-Type Fructans from Artichoke Wastes and Their Effect on the Growth of Intestinal Bacteria Associated with Health

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Zahraa Zeaiter ◽  
Maria Elena Regonesi ◽  
Sofia Cavini ◽  
Massimo Labra ◽  
Guido Sello ◽  
...  
Keyword(s):  
Intestinal Bacteria ◽  
Degree Of Polymerization ◽  
Average Degree ◽  
Globe Artichoke ◽  
Ethanol Precipitation ◽  
Long Chain ◽  
Simpler Method

Globe artichoke is an intriguing source of indigestible sugar polymers such as inulin-type fructans. In this study, the effect of ultrasound in combination with ethanol precipitation to enhance the extraction of long chain fructans from artichoke wastes has been evaluated. The inulin-type fructans content both from bracts and stems was measured using an enzymatic fructanase-based assay, while its average degree of polymerization (DP) was determined by HPLC-RID analysis. Results show that this method provides artichoke extracts with an inulin-type fructans content of 70% with an average DP between 32 and 42 both in bracts and in stems. The prebiotic effect of long chain inulins from artichoke extract wastes was demonstrated by its ability to support the growth of five Lactobacillus and four Bifidobacterium species, previously characterized as probiotics. Besides, we considered the possibility to industrialize the process developing a simpler method for the production of inulin-type fructans from the artichoke wastes so that the artichoke inulin preparation could be suitable for its use in synbiotic formulations in combination with different probiotics for further studies including in vivo trials.

Reverberation Intensity Decaying in Range-Dependent Waveguide

2019 ◽  
Vol 27 (03) ◽  
pp. 1950007
Author(s):  
J. R. Wu ◽  
T. F. Gao ◽  
E. C. Shang
Keyword(s):  
Large Scale ◽  
Back Propagation ◽  
Normal Modes ◽  
Small Scale ◽  
Signal Pulse ◽  
First Order ◽  
Orthogonal Property ◽  
Short Signal ◽  
Scale Roughness ◽  
Special Case

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

Time course and vectorial nature of albumin metabolism in isolated perfused rabbit PCT

1988 ◽  
Vol 255 (3) ◽  
pp. F520-F528 ◽  
Author(s):  
C. H. Park
Keyword(s):  
Time Course ◽  
Hydrolysis Product ◽  
High Capacity ◽  
Intact Protein ◽  
Renal Metabolism ◽  
First Order ◽  
First Order Kinetics ◽  
Hydrolysis Products ◽  
Renal Tubular ◽  
Hydrolysis Of

The time course and vectorial nature of renal metabolism of albumin (Alb) were studied. The tubular absorption, accumulation, and hydrolysis of Alb and the release of the hydrolysis products were determined in the isolated rabbit proximal convoluted tubule (PCT) perfused with tritiated Alb ([3H3C]Alb) at 36.4 micrograms/ml. The Alb absorption across the apical membrane was constant (99.9 +/- 4.9 x 10(-3) ng.min-1.mm-1). In contrast, the accumulation and hydrolysis of Alb in the cells increased nonlinearly with time. The bulk of the tritium that accumulated in the cells was associated with intact [3H3C]Alb. Only the final hydrolysis products were released from the cells and these first appeared in the peritubular bath 6–7 min after the start of perfusion of the tubule with [3H3C]Alb. The hydrolysis product was not detectable in the tubule lumen. The proteolytic activity correlated linearly with the protein load to the cells, characteristic of first-order kinetics and a high-capacity system. The results suggest that the renal tubular handling of proteins proceeds from the apical to the basolateral aspect of the cell. The transcellular processing of Alb is rapid and can occur in 6–7 min. The accumulation of intact protein in the cell and the first-order kinetics of hydrolysis of the absorbed protein suggest that the rate-limiting step in proximal tubular handling of proteins may include the initial hydrolysis of protein or reside in steps that precede the hydrolysis.

scholarly journals Population Pharmacokinetics of Oseltamivir: Pediatrics through Geriatrics

2013 ◽  
Vol 57 (8) ◽  
pp. 3470-3477 ◽  
Author(s):  
Mohamed A. Kamal ◽  
Scott A. Van Wart ◽  
Craig R. Rayner ◽  
Vishak Subramoney ◽  
Daniel K. Reynolds ◽  
...  
Keyword(s):  
Steady State ◽  
Time Course ◽  
Demographic Data ◽  
Visual Predictive Check ◽  
Compartment Model ◽  
Plasma Drug ◽  
First Order ◽  
Drug Concentrations ◽  
Population Pk ◽  
The Impact

ABSTRACTOseltamivir is a potent inhibitor of influenza virus neuraminidase enzymes essential for viral replication. This study aimed to investigate the impact of covariates on pharmacokinetic (PK) variability of oseltamivir and its active metabolite form, oseltamivir carboxylate (OC). Dosing history, plasma drug concentrations, and demographic information were pooled from 13 clinical trials providing data for 390 healthy and infected subjects ranging in age from 1 to 78 years and given oseltamivir doses of 20 to 1,000 mg. Candidate population PK models simultaneously characterizing the time course of oseltamivir and OC in plasma were evaluated by using the NONMEM software program, and subject covariates were assessed using stepwise forward selection (α = 0.01) and backward elimination (α = 0.001). A two-compartment model with first-order absorption of oseltamivir and first-order conversion of oseltamivir to OC and a one-compartment model with first-order elimination of OC were utilized. Body weight when evaluated using a power function was a significant predictor of the apparent oseltamivir clearance and both apparent OC clearance (CLm/F) and central volume of distribution (Vcm/F). Creatinine clearance was a significant predictor of CLm/F, while Vcm/F also decreased linearly with age. A visual predictive check indicated that the final model described oseltamivir and OC concentrations in plasma adequately across dose regimens and subject covariate ranges. Concordance of population mean and individualpost hocpredictions of maximum concentration of drug at steady state (Cmax) and area under the plasma drug concentration-time curve from 0 to 24 h at steady state (AUC0–24) was high (r2= 0.81 and 0.71, respectively). In conclusion, a comprehensive population PK model was constructed to bridge the adult to pediatric oseltamivir PK data, allowing for reasonable estimation of the PK of OC using subject demographic data alone.

Sign in / Sign up

Export Citation Format

Share Document