Homogeneous rectangular tessellations

1996 ◽  
Vol 28 (4) ◽  
pp. 993-1013 ◽  
Author(s):  
Margaret S. Mackisack ◽  
Roger E. Miles
Keyword(s):  
Blocking Effect ◽  
Basic Theory ◽  
Isotropic Model ◽  
Mean Values ◽  
First Order ◽  
Multi Stage ◽  
True Model

A rectangular tessellation is a covering of the plane by non-overlapping rectangles. A basic theory for general homogeneous random rectangular tessellations is developed, and it is shown that many first-order mean values may be expressed in terms of just three basic quantities. Corresponding values for independent superpositions of two or more such tessellations are derived. The most interesting homogeneous rectangular tessellations are those with only T-vertices (i.e. no X-vertices). Gilbert's (1967) isotropic model adapted to this two-orthogonal-orientations case, although simply specified, appears theoretically intractable, due to a complex ‘blocking' effect. However, the approximating penetration model, also introduced by Gilbert, is found to be both tractable and informative about the true model. A multi-stage method for simulating the model is developed, and the distributions of important characteristics estimated.

Homogeneous rectangular tessellations

1996 ◽  
Vol 28 (04) ◽  
pp. 993-1013 ◽  
Author(s):  
Margaret S. Mackisack ◽  
Roger E. Miles
Keyword(s):  
Blocking Effect ◽  
Basic Theory ◽  
Isotropic Model ◽  
Mean Values ◽  
First Order ◽  
Multi Stage ◽  
True Model

A rectangular tessellation is a covering of the plane by non-overlapping rectangles. A basic theory for general homogeneous random rectangular tessellations is developed, and it is shown that many first-order mean values may be expressed in terms of just three basic quantities. Corresponding values for independent superpositions of two or more such tessellations are derived. The most interesting homogeneous rectangular tessellations are those with only T-vertices (i.e. no X-vertices). Gilbert's (1967) isotropic model adapted to this two-orthogonal-orientations case, although simply specified, appears theoretically intractable, due to a complex ‘blocking' effect. However, the approximating penetration model, also introduced by Gilbert, is found to be both tractable and informative about the true model. A multi-stage method for simulating the model is developed, and the distributions of important characteristics estimated.

scholarly journals Estimation of Levocetirizine in Bulk and Formulation by First Order Derivative Area under Curve UV-Spectrophotometric Methods.

2016 ◽  
Vol 2 (1) ◽  
pp. 09
Author(s):  
Pandurang Tukaram Mane
Keyword(s):  
Area Under Curve ◽  
Pharmaceutical Formulations ◽  
Order Derivative ◽  
Pharmaceutical Dosage Forms ◽  
Mean Values ◽  
First Order ◽  
Spectrophotometric Methods ◽  
Ich Guidelines ◽  
Significant Difference

Simple, fast and reliable spectrophotometric methods were developed for determination of Levocetirizine in bulk and pharmaceutical dosage forms. The solutions of standard and the sample were prepared in Methanol. The quantitative determination of the drug was carried out using the second order Derivative Area under Curve method values measured at 235-243 nm. Calibration graphs constructed at their wavelengths of determination were linear in the concentration range of Levocetirizine using 5-25?g/ml (r=0.9994) for first order Derivative Area under Curve spectrophotometric method. The proposed methods have been extensively validated as per ICH guidelines. There was no significant difference between the performance of the proposed methods regarding the mean values and standard deviations. The developed methods were successfully applied to estimate the amount of Levocetirizine in pharmaceutical formulations.

National Survey of Caries Prevalence in 6-15-year-old Children in France

1989 ◽  
Vol 68 (1) ◽  
pp. 64-68 ◽  
Author(s):  
P.M. Cahen ◽  
J.C. Turlot ◽  
R.M. Frank ◽  
A.M. Obry-Musset
Keyword(s):  
Dental Health ◽  
Epidemiological Studies ◽  
Age Group ◽  
Dental Surgery ◽  
Mean Values ◽  
Multi Stage ◽  
Dmft Index ◽  
The Mean ◽  
Carious Teeth ◽  
Baseline Examination

The prevalence of dental caries in France is not known on a nationwide basis, despite the fact that a number of epidemiological studies have been conducted in various parts of the country. The aim of the present study was to provide a national baseline examination of the dental health of children in 1987 since, beginning in November, 1986, the sale of fluoridated salt began in France. A multi-stage probability sample of 19,366 children was selected as representative of the 6-to-15-year-old population. The sample covered all the 95 departments of France. Teams of well-calibrated examiners were constituted in each of the sixteen Faculties of Dental Surgery of France. The prevalence of caries for each age group was determined by means of DMFT, DMFS, dft, and dfs indices. Periodontal conditions were assessed by means of the Plaque Index (Silness and Löe, 1964), the Calculus Index (Marthaler, 1966), and the Gingival Index (Löe and Silness, 1963). Calculation of the mean DMFT index showed, respectively, 0.5 and 1.0 new carious teeth per year under and over the age of 11. The mean values of the DMFT index at ages 6, 12, and 15 were, respectively, 0.5, 4.2, and 6.9. Under the age of 11, the mean DMFS index increased by one between each successive age group and by nearly two over the age of 11. The mean values of the DMFS index at ages 6, 12, and 15 were, respectively, 0.8, 7.6, and 13.0. The percentage of caries-free children decreased from 32.2% at age 6 to 7.9% at age 15.

The direct calculation of the first-order density matrix for atoms

1965 ◽  
Vol 283 (1393) ◽  
pp. 194-202 ◽  
Keyword(s):  
Perturbation Theory ◽  
Density Matrix ◽  
Ground State ◽  
Direct Calculation ◽  
Molecular Orbitals ◽  
Natural Orbitals ◽  
Mean Values ◽  
First Order ◽  
Order Contribution

The theory of isoelectronic sequences of atoms has been developed as a perturbation theory and is extended here to the calculation of the first-order density matrix. It is shown that the calculation of the first-order contribution to this matrix can be reduced to the solution of a number of one-electron equations. These equations have been solved for the helium ground state, the helium 3 S state and the lithium ground state. From the density matrix, mean values of one-electron operators can be derived by integration. A variety of these mean values is quoted and the significance of the stable values discussed. From the density matrix the natural orbitals can be derived and these are found to be identical with the unrestricted molecular orbitals to terms of zero and first order.

Critical antiferromagnetic square-lattice Potts model

1982 ◽  
Vol 383 (1784) ◽  
pp. 43-54 ◽  
Keyword(s):  
Free Energy ◽  
Critical Temperature ◽  
Internal Energy ◽  
Latent Heat ◽  
Potts Model ◽  
Square Lattice ◽  
Isotropic Model ◽  
First Order

The critical temperature of the antiferromagnetic q -state Potts model on the square lattice is located, and the critical free energy and internal energy are evaluated. As with the ferromagnetic model, the transition is continuous for q ≼4, and its first-order (i. e. has latent heat) for q >4. However, only for q ≼3 can the critical temperature be real. For the isotropic model the criticality condition is exp( J / k T ) = -1 + (4- q ) ½ .

scholarly journals Development of Chinese VAS Value Set for EQ-5D-3L and Difference analysis with the TTO Value Set Based on Same Nationally Representative Sample

2021 ◽  
Author(s):  
Lang Zhuo ◽  
Lin Zhuo ◽  
Siting Chen ◽  
Ting Cai ◽  
Jianqiang Pan ◽  
...  
Keyword(s):  
Representative Sample ◽  
Chinese Population ◽  
Goodness Of Fit ◽  
Absolute Error ◽  
Original Data ◽  
Least Square ◽  
Mean Values ◽  
Value Set ◽  
Multi Stage ◽  
Nationally Representative

Abstract Objective: To develop a Chinese VAS value set for EQ-5D-3L and compare it with the TTO value set based on nationally representative sample. Methods: An adapted Measurement and Valuation of Health (MVH) protocol was applied with VAS method. EQ-5D-3L was used in face-to-face interviews conducted by trained interviewers with participants selected via multi-stage stratified clustered random sample. Fifteen hypothetical health statuses (11 random states in MVH protocol, plus 11111, 33333, unconscious and death) were assigned for assessment individually. Ordinary least square, general least square and weighted least square models were constructed with or without N3. Four categories of indices, including quality of original data, distribution of rescaled values, goodness of fit of models, and distribution of predicted values were adopted to compare between Chinese VAS and TTO value sets.Results: All 5,939 participants aged 15 and over were interviewed; 5,884 eligible participants were included in constructing models. An OLS model that included ten dummy variables and a constant and without N3 was chosen as the best-fit VAS model (Adjusted R2=0.670). The mean absolute error was 0.0319, and the correlation coefficient between predicted and mean values was 0.9837. The curve of predicted value of VAS model was uniformly lower than that of Chinese TTO value set. Comparing with the TTO value set, VAS method had higher responsive rate, less inconsistency, lower skewed values and better goodness of fit values. Conclusions: VAS value set performed rationally in Chinese population for its simplicity, responsiveness and robustness. We recommend the VAS value set, Model 2, as the benchmark of scoring algorithm of HRQoL for Chinese population.

scholarly journals Peculiarities of the postoperative period and postoperative consequences of left hemicolectomy in patients with obesity

2021 ◽  
Vol 25 (1) ◽  
pp. 45-49
Author(s):  
A. I. Sukhodolia ◽  
V. V. Kernychnyi ◽  
V. V. Balytskyi ◽  
S. A. Sukhodolia ◽  
B. E. Li
Keyword(s):  
Postoperative Complications ◽  
Postoperative Period ◽  
Postoperative Mortality ◽  
Charlson Index ◽  
Obese Patients ◽  
Microsoft Excel ◽  
Mean Values ◽  
Left Hemicolectomy ◽  
Multi Stage ◽  
The Impact

Annotation. Obesity is considered a risk factor for postoperative complications and postoperative mortality. The aim of the study was to assess the impact of obesity on the postoperative period and the level of postoperative mortality after left hemicolectomy. A retrospective analysis of the medical records of 217 patients who underwent left hemicolectomy for colon tumors was performed. Assessment of comorbid conditions was performed using the Charlson index. Postoperative complications were assessed according to the Clavien-Dindo classification. The calculation of postoperative survival was performed by the Kaplan-Mayer method. Database formation and statistical analysis were performed using Microsoft Excel and STATISTICA 10.0. It was determined that the mean values of the Charlson index did not differ significantly between the two groups (6,31 ± 2,07 and 6,33 ± 2,08 respectively), but there was a significantly higher level of endocrine diseases in the group of obese patients. Non-disseminated (I-II) stages of the tumor process predominated in patients of both groups (60% and 57.5%, respectively). Among non-obese patients n = 107 (51.8%) patients had an uncomplicated postoperative period and n = 59 (28.5%) patients had mild complications that were not associated with the surgical site, but were associated with concomitant chronic pathology of other organs and systems, and did not require any invasive interventions. In contrast, among obese patients n = 6 (60%) patients had severe early postoperative complications requiring surgery, and n = 2 (20%) patients underwent relaparotomy. The rate of early postoperative mortality differed significantly between the two groups and was significantly higher among obese patients (40% vs 6.8% among non-obese patients). This study showed a significantly higher percentage of postoperative mortality and severity of postoperative complications in the group of obese patients. The prospect of further research is to study and analyze the course of the postoperative period in obese patients undergoing extended, multi-visceral and multi-stage surgery for cancer of the left half of the colon.

Topos-theoretic background

2018 ◽  
Author(s):  
Olivia Caramello
Keyword(s):  
Category Theory ◽  
Order Theory ◽  
Order Logic ◽  
Basic Theory ◽  
First Order Logic ◽  
Syntactic Category ◽  
First Order ◽  
Deductive Systems ◽  
First Order Theory ◽  
Categorical Semantics

This chapter provides the topos-theoretic background necessary for understanding the contents of the book; the presentation is self-contained and only assumes a basic familiarity with the language of category theory. The chapter begins by reviewing the basic theory of Grothendieck toposes, including the fundamental equivalence between geometric morphisms and flat functors. Then it presents the notion of first-order theory and the various deductive systems for fragments of first-order logic that will be considered in the course of the book, notably including that of geometric logic. Further, it discusses categorical semantics, i.e. the interpretation of first-order theories in categories possessing ‘enough’ structure. Lastly, the key concept of syntactic category of a first-order theory is reviewed; this notion will be used in Chapter 2 for constructing classifying toposes of geometric theories.

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