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# Convert to Regular Notation 6.3*10^-11

6.3×10-11
Since the exponent of the scientific notation is negative, move the decimal point 11 places to the left.
0.000000000063
Convert to Regular Notation 6.3*10^-11


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# arithmetic sequence/ functions

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1. The first and thirteenth terms of an arithmetic sequence are $$\frac{7}{9}$$ and $$\frac{4}{5}$$, respectively. What is the seventh term?

2. If the point (3,6) is on the graph of $$y=g(x)$$, and $$h(x)=(g(x))^2$$ for all x, then there is one point that must be on the graph of $$y=h(x)$$ .What is the sum of the coordinates of that point?

mathtoo  Aug 28, 2018
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1. The first and thirteenth terms of an arithmetic sequence are  7/9  and 4/5 , respectively. What is the seventh term?

We have that

4/5  =  7/9 + d (12)

4/5 - 7/9 =  d (12)

1/45  = d(12)

1 (45 *12)  = d

1/540  = d

So...the seventh term is....    7/9  + (1/540)(6)    = 71 / 90

CPhill  Aug 28, 2018

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# How do you differentiate f(t)= sqrt(ln(t)) / (-4t-6)^2 using the quotient rule?

Jan 11, 2018

$f ' \left(t\right) = \frac{\left(- 4 t - 6\right) + 16 t \ln t}{2 t \sqrt{\ln t} {\left(- 4 t - 6\right)}^{3}}$

#### Explanation:

For the quotient rule:

$f \left(t\right) = u v \to f ' \left(t\right) = \frac{u ' v - u v '}{v} ^ 2$

So

u = sqrt(ln(t))-> u'=1/(2tsqrt(ln(t))

And:

$v = {\left(- 4 t - 6\right)}^{2} \to v ' = - 8 \left(- 4 t - 6\right)$

Using the quotient rule:

$f ' \left(t\right) = \frac{\frac{1}{2 t \sqrt{\ln t}} {\left(- 4 t - 6\right)}^{2} + 8 \sqrt{\ln \left(t\right)} \left(- 4 t - 6\right)}{- 4 t - 6} ^ 4$

$= \frac{\frac{{\left(- 4 t - 6\right)}^{2} + 16 t \ln t \left(- 4 t - 6\right)}{2 t \sqrt{\ln t}}}{- 4 t - 6} ^ 4$

Simplifying by canceling a factor of $\left(- 4 t - 6\right)$:

$= \frac{\left(- 4 t - 6\right) + 16 t \ln t}{2 t \sqrt{\ln t} {\left(- 4 t - 6\right)}^{3}}$


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# Abstracts

Criança; Uso de Medicamentos; Fatores Socioeconômicos; Desigualdades em Saúde; Estudos Transversais; Farmacoepidemiologia

Niño; Utilización de Medicamentos; Factores Socioeconómicos; Desigualdades en la Salud; Estudios Transversales; Farmacoepidemiología

OBJECTIVE: To describe drug use profile in children living in poor areas and associated factors. METHODS: Population-based, cross-sectional study, including 1,382 children aged between four and 11 years. These children were selected by random sampling of 24 micro-areas, representative of the poorest segments of the population living in the city of Salvador, Northeastern Brazil, in 2006. The dependent variable was drug use in the 15 days preceding the surveys. A total of three groups of explanatory variables were considered: socioeconomic variables, child health status, and use of health services. Adjusted analysis used Poisson regression, following a hierarchical conceptual model. RESULTS: Drug use prevalence in children was 48%. Female children showed higher drug use prevalence than males, 50.9% and 45.4%, respectively (p=0.004). Drug use prevalence decreased significantly with age (p<0.001) in both sexes. Most used pharmacological groups were: analgesics/antipyretics (25.5%), systemic antibiotics (6.5%), and anti-cough /expectorant drugs (6.2%). In the multivariate analysis, factors determining greater drug use were: age (four to five, six, seven to eight years); female sex; white mother; poorer health perception; interruption of activities due to health problems and health care, whether ill or not, in the last 15 days; drug spending in the last month; and medical visits in the last three months. CONCLUSIONS: Drug use prevalence in the poor children studied was below that observed in other population-based studies in Brazil, yet similar to that of adults. The identification of groups most subject to excessive drug use may serve as the basis for strategies to promote their rational use.

Child; Drug Utilization; Socioeconomic Factors; Health Inequalities; Cross-Sectional Studies; Pharmacoepidemiology

ORIGINAL ARTICLES

Drug use and associated factors in children living in poor areas

Utilización de medicamentos y factores asociados entre niños residentes en áreas pobres

Djanilson Barbosa SantosI; Mauricio Lima BarretoII; Helena Lutescia Luna CoelhoIII

ICentro de Ciências da Saúde. Universidade Federal do Recôncavo da Bahia. Santo Antônio de Jesus, BA, Brasil

Correspondence

ABSTRACT

OBJECTIVE: To describe drug use profile in children living in poor areas and associated factors.

METHODS: Population-based, cross-sectional study, including 1,382 children aged between four and 11 years. These children were selected by random sampling of 24 micro-areas, representative of the poorest segments of the population living in the city of Salvador, Northeastern Brazil, in 2006. The dependent variable was drug use in the 15 days preceding the surveys. A total of three groups of explanatory variables were considered: socioeconomic variables, child health status, and use of health services. Adjusted analysis used Poisson regression, following a hierarchical conceptual model.

RESULTS: Drug use prevalence in children was 48%. Female children showed higher drug use prevalence than males, 50.9% and 45.4%, respectively (p=0.004). Drug use prevalence decreased significantly with age (p<0.001) in both sexes. Most used pharmacological groups were: analgesics/antipyretics (25.5%), systemic antibiotics (6.5%), and anti-cough /expectorant drugs (6.2%). In the multivariate analysis, factors determining greater drug use were: age (four to five, six, seven to eight years); female sex; white mother; poorer health perception; interruption of activities due to health problems and health care, whether ill or not, in the last 15 days; drug spending in the last month; and medical visits in the last three months.

CONCLUSIONS: Drug use prevalence in the poor children studied was below that observed in other population-based studies in Brazil, yet similar to that of adults. The identification of groups most subject to excessive drug use may serve as the basis for strategies to promote their rational use.

Descriptors: Child. Drug Utilization. Socioeconomic Factors. Health Inequalities. Cross-Sectional Studies. Pharmacoepidemiology.

RESUMEN

OBJETIVO: Describir el perfil de uso de medicamentos entre niños residentes en áreas pobres y factores asociados.

MÉTODOS: Estudio transversal de base poblacional que incluyó 1.382 niños entre cuatro y 11 años de edad, seleccionadas por muestreo aleatorio de 24 micro-áreas representativas de las zonas más pobres de la población residente en el municipio de Salvador, Noreste de Brasil, en 2006. La variable dependiente fue el consumo de medicamentos en los 15 días anteriores a la realización de las pesquisas. Fueron considerados tres grupos de variables explicatorios: socioeconómicas, estado de salud del niño y utilización de los servicios de salud. El análisis ajustado utilizó regresión de Poisson siguiendo un modelo conceptual jerarquizado.

RESULTADOS: La prevalencia de consumo de medicamentos en niños fue de 48%. Los niños del sexo femenino presentaron prevalencia de utilización de medicamentos superior al sexo masculino, 50,9% y 45,4%, respectivamente (p=0,004). La prevalencia de uso de medicamentos disminuyó significativamente con la edad (<0,001) en ambos sexos. Los grupos farmacológicos más utilizados fueron los analgésicos/antitérmicos (25,5%), antibacterianos sistémicos (6,5%) y antitusígenos/expectorantes (6,2%). En el análisis multivariado los factores determinantes de mayor utilización de medicamentos fueron: edad (cuatro a cinco, seis, siete a ocho años), sexo femenino, madres de color de piel blanca, peor percepción de salud, interrupción de actividades por problemas de salud y atención de salud independientemente de estar enfermo en los últimos 15 días, gasto con medicamentos en el último mes y realización de consultas con médico en los últimos tres meses.

CONCLUSIONES: La prevalencia de uso de medicamentos entre niños pobres estudiados fue inferior a la verificada en otros estudios poblacionales en Brasil, pero semejante a la de adultos. La identificación de grupos más sujetos al uso excesivo de medicamentos puede justificar estrategias para promoción de su uso racional.

Descriptores: Niño. Utilización de Medicamentos. Factores Socioeconómicos. Desigualdades en la Salud. Estudios Transversales. Farmacoepidemiología.

INTRODUCTION

In developing countries, children are the main health service users and the first to suffer the impact of changes in the health-disease process in the community9 and their pattern of illness is reflected on drug use. This use, in its turn, can be considered an indirect indicator of health service quality and is expected to contribute to service or treatment effectiveness.17

In the case of children, rational drug use must take into consideration the specificities of age sub-groups and the peculiarities of their development. The practice of drug use in children is mostly based on extrapolations and adaptations of use in adults, information obtained from rare observational studies, consensus from experts and clinical assays in this population.7,23,24

Although necessary, studies on the prevalence of drug use in children are yet scarce.5,8,14,15,25 In an extensive investigation conducted in England with children aged between zero and 7.5 years of age, Headley & Northstone14 found out that three quarters of the sample had used medicinal products before eight weeks of age.

In the city of Pelotas, Southern Brazil, Béria et al,5 studied 4,746 children aged from two to six years and observed a drug use prevalence of 56% in the period of 15 days preceding the interview. In municipal day care centers of the city of São Paulo, Southeastern Brazil, Bricks & Leoni8 analyzed 1,382 children aged between two and seven years and observed a drug use prevalence of 37% in the last two months. In Pelotas, Weiderpass et al25 studied 655 children in their first and third months of life, with drug use prevalences of 65% and 69%, respectively, in the two weeks preceding the interviews conducted with the mothers. All these three studies found an association between drug use and children sex and age, maternal level of education, firstborns and use of health services.5,8,25

The present study aimed to describe the drug use profile of children living in poor areas and its associated factors.

METHODS

A cross-sectional, population-based study in a cohort of children was performed in the urban area of the city of Salvador, Northeastern Brazil, between February and May 2006. This study was part of the more extensive research project, entitled "Social Changes, Asthma and Allergy in Latin America" (SCAALA), on risk factors for asthma and allergy in children aged between four and 11 years in Brazil, whose characteristics were described elsewhere.3

The study population was selected by a random sample of 24 micro-areas, representative of the poorest regions in Salvador where the population lives. The sample of children was obtained from two epidemiological surveys. The first one was conducted with children aged between zero and four years of age, from 2000 to 2002, and aimed to assess the impact of the sanitation program on children's health conditions in Salvador.25 This cohort was investigated in a second epidemiological survey of risk factors for asthma and allergy, conducted in 2005, which characterized the SCAALA project3 study population. Thus, during the period of home interviews in 2006, 1,382 children aged between four and 11 years participated in the study, comprising 95.6% of the initial cohort of the SCAALA project (1,445 children).3 A total of 63 children were excluded from the analysis: 26 could not be located due to change of address and 37 did not have information about the mothers.

The instrument used for data collection was a structured questionnaire, including questions about drug use, maternal and child sociodemographic characteristics, child health status and use of health services.

Questionnaires were applied using home interviews, conducted with the mothers or those responsible for the children. In the absence of a responsible adult, interviewers returned at least two times to the homes. When these attempts failed, the visit was made by the field supervisor. During application of the questionnaire on information about drug use in the last 15 days, mothers or those responsible were requested to show the medical prescription and the package of the drugs used, when available, in order to note down the product characteristics correctly. Drugs whose prescriptions and packages were not available at the moment of the interview at home, but which were reported by the mothers as having been used, were also considered.

Drug use in the 15 days preceding the interview was the dependent variable. This outcome was defined by the following question: "Did the child use any medication in the last 15 days? Give an example. Drugs for fevers, headaches, vomit, diarrhea and infection. Drugs such as vitamins and tonics (Attention: exclude homemade remedies/teas, magistral formulas and phytotherapeutic agents)". Drugs were broken down into their active principles and classified according to the Anatomical Therapeutic Chemical Index (ATC/DDD Index), developed by the World Health Organization Collaborating Center for Drug Statistics Methodology.ª a World Health Organization. WHO Collaborating Centre for Drug Statistics Methodology [internet]. Oslo; 2001[cited 2008 May 01]. Available from: http://www.whocc.no

Independent variables were categorized into three levels. The first level was comprised of socioeconomic variables: maternal ethnicity (white, black), maternal level of education (zero to four, five to eight, nine or more years of study), maternal occupation related to the practice of paid activities (yes: civil servant; military professional; business owner; self-employed professional; worker in retail, factory or services; retired and pension plan holder/ no: unemployed; housewife; student), monthly family income (up to one, from one to two, and from two to five minimum wages - MW), maternal age (15 to 29, 30 to 39, 40 to 79 years). The Brazilian minimum wage at the time of this study was R$300.00 per month (approximately US$ 160.00).

The second level was comprised of child health status variables: health perception reported by the mother (excellent/very good, good, poor/very poor), diseases or chronic conditions reported by the mother to investigate the medical diagnosis history (asthma, pulmonary tuberculosis, pneumonia, hepatitis, arterial hypertension, urinary infection, chronic renal disease), interruption of activities/school absence due to health problems in the last 15 days (yes, no).

The third level was comprised of health service use variables: medical consultations in the last three months (none, one, two or more); pharmaceutical consultations in the last three months (yes, no); hospitalizations in the last 12 months (yes, no); private health plan (yes, no); child received health care in the last 15 days, whether ill or not (yes, no); and drug spending in the last month (yes, no). The child age (four to five, six, seven to eight, nine to 11 years) and sex (male and female) demographic variables were considered potential confounding factors.

In data analysis, drug use prevalence according to sex and age group was estimated from the proportion of children who had taken at least one drug in the last 15 days, divided by the total number of children per sex in each age group.

In the bivariate analysis, the chi-square test was used to compare proportions (Mantel-Haentzel), while the linear trend test was used for ordinal variables. Multiple logistic regression analysis was performed, using the robust Poisson regression method for the "drug use" dependent variable: (0) did not use drugs and (1) used drugs. This analysis followed the proposed hierarchical conceptual model. On all hierarchical levels in the adjusted analysis, the sex and age variables were included, which remained in the model for the adjustment of variables of all hierarchical levels, even when they were not significant. On the subsequent levels, variables that continued to be associated with drug use, after adjustment for confounding variables in the same block and those hierarchically higher, remained in the model.

All variables that were associated with the dependent variable, with a level of statistical significance p<0.20 to control confounding factors, remained in the regression model. Variables associated with drug use on a level p<0.05 remained in the final model. Sampling design effect was considered in all analyses, using the set of svy commands, specific for the analysis of surveys based on Stata 9.0 statistical software complex samples.

This study was approved by the Comitê de Ética do Instituto de Saúde Coletiva da Universidade Federal da Bahia (Bahia Federal University Institute of Collective Health Ethics Committee). Mothers or adults responsible for the children answered the questionnaire after signing an informed consent form.

RESULTS

Of all the 1,382 children studied, 663 (48%) had taken drugs in the last 15 days, according to what mothers reported. The number of drugs (occurrence of reports) taken was 1,030, totaling 269 different commercial names for 113 active principles. Of all the 663 children, 63% had used one drug, 24% had used two, and 13% three or more. Of all the 1,030 drugs, 467 (45.3%) were given to children based on their mothers' decision; 439 (42.6%) were recommended by doctors, 82 (8.0%) by relatives, friends and neighbors and 25 (2.4%) by pharmacists; ten (1.0%) were due to influence of commercial advertisements (radio, television, magazines) and four (0.4%) whose source the mother could not inform.

The majority of drugs (67%) were acquired in private pharmaceutical establishments; 14% in health clinic drugstores; 10% the mother had at home; 4% were free samples received from doctors, 3% from hospital/outpatient clinic drugstores and 2% were drugs partially subsidized by a special program. Of all the active principles, only 58.4% were included in the Relação Nacional de Medicamentos Essenciais (RENAME - Brazilian Inventory of Essential Drugs, 2007).b b Ministério da Saúde. Departamento de Assistência Farmacêutica e Insumos Estratégicos. Relação nacional de medicamentos. 4. ed. Brasília; 2007. Of all the products, 70 (26%) were inadequate for use in children, including anti-cough drugs, decongestants, iodide syrups, expectorants and mucolytics.

Table 1 shows that female children have a drug use prevalence which is always higher than that of males, 50.9% and 45.4%, respectively (p=0.004). Drug use prevalence significantly decreased with age (p<0.001) in both sexes; in the extreme age groups in which the study population was characterized, 4-5 years and 9-11 years, prevalence decreased from 60.9% to 43.3% among females (p=0.003) and from 55.1% to 35.6% among males (p<0.001).

The most frequently reasons for drug use were as follows: fever (28.8%), cough (8.3%), flu/cold (7.9%), sore throat (7.2%), headache (7.0%) and tiredness (6.2%). According to the first level of ATC classification, the three main anatomical groups most frequently used were: drugs that function in the central nervous system (26.4%), drugs that function in the respiratory system (15.1%), and anti-infective drugs for systemic use (6.6%). Table 2 shows the prevalence of use of pharmacological groups and active principles.

In the bivariate analysis, the prevalence and factors associated with drug use were higher and statistically significant in children aged 4-5 years (57.9%), female sex (50.9%), those whose mothers had a professional activity (52.2%), poor/very poor child health perception, reported by the mother (79.7%), presence of chronic diseases/conditions reported by the mother (53.9%), and those who interrupted their activities or missed school due to health problems in the last 15 days (84.7%) (Table 3). In terms of use of health services, drug use was higher in children who had two or more medical consultations in the last three months (63.9%); those who received health care, whether ill or not, in the last 15 days (69.8%); those who had been hospitalized in the last 12 months (56.5%); and those who had spent money on drugs in the last months (77.2%)

In all multiple logistic regression stages (Table 3), the hierarchical model variables were adjusted for child age and sex. In the first stage, the socioeconomic variable - black mothers - after adjustment for child age and sex, maintained the bivariate analysis findings, except for maternal occupation, which maintained a positive association, though not statistically significant. Ethnicity, monthly family income (2-5 MW) and maternal occupation remained for the subsequent analysis (p<0.20).

In the second stage, the effect of child health status was adjusted from age, sex and socioeconomic variables (ethnicity, monthly family income between 2-5 MW and maternal occupation). Children who missed school in the last 15 days due to health problems and those who had the poorest health perception reported by the mother maintained the statistical significance observed in the bivariate analysis, even though both lost strength of association.

"Health perception reported by the mother", "chronic disease" and "interruption of activities/school absence due to health problems in the last 15 days" remained in the third stage. In the last stage, "medical consultations in the last three months", "children who received health care, whether ill or not" and "mothers who reported drug spending in the last months" continued to be positively and significantly associated, according to bivariate analysis.

All variables mentioned lost strength of association. "Hospitalization of children in the last 12 months" continued to be positively associated, after adjustment by possible confounding factors, although without statistical significance.

Table 4 shows the final results of multiple logistic regression analysis of factors associated with drug use in children. After adjusted analysis, the following were the associated factors: age (4-5, six and 7-8 years); female sex; black mothers; poorer health perception reported by the mother; interruption of activities/school absence due to health problems; health care, whether ill or not; drug spending; and medical consultations in the last three months.

DISCUSSION

Drug use prevalence in children aged from four to 11 years, estimated in the present study, was 48%, based on information about a 15-day recall period provided by the mother. Some sample characteristics need to be considered when compared to literature data, once socioeconomic conditions are known drug use determinants.2,6 Among these conditions, the fact that the population studied lives in a major city of Northeast Brazil should be considered, as this city is little heterogeneous in economic terms, not including society's most privileged classes as regards income, education and health service access. As this study concerns a household survey, it was possible to collect detailed information such as the checking of prescriptions and drugs/drug packages that have remained, as well as to return to a home to complement information, guaranteeing data quality.

Drug use prevalence in the population studied was above the 37% found by similar research, performed in 15 public day care centers in the city of São Paulo,8 and above the 25.4% drug use prevalence in the last two days of a study performed in Spain with children aged younger than 15 years.20 However, the drug use prevalence found in this study was below those identified by Béria et al (54%)5 between 35 and 53 months of life and Weiderpass et al (69%)26 in the first and third months of life in Brazilian studies. In addition, it was below the 60% prevalence of use of at least one drug in the last 12 months in children aged between zero and 16 years, in Holland.22 These studies included children younger than four years,5,8,20,22,26 three were based on information reported by the mothers,5,8,26 four were population-based studies5,8,20,26 and the recall period varied from two days to 12 months, hindering comparison with the results from this study.

In the present study, findings related to age were in agreement with the literature in terms of the progressive decrease in drug use prevalence with the increase in age group.5,8,11,12 In addition, drug use decreased with age, being higher among children aged between four and five years, compared to the remaining age groups.

In terms of sex, the present study revealed that drug use among females was higher than among male children, in all age groups. This finding is similar to that found in adults, among whom drug use differences between sexes have been explained by sociocultural and biological aspects that would cause more illness and self-care, and higher search for health services and exposure to drugs in women.2,6,11,12 However, some of these factors, such as disorders associated with reproductive life and the family health caregiver's social role, would not apply to female children. On the other hand, some studies have shown higher general drug use prevalence in male children, suggesting the presence of specific cultural or biological aspects in the population focused by the present study.8,16

According to what was informed by mothers, 50.2% of drugs used had been recommended by doctors and 45.7% had been decided by the mothers themselves, of which 67% were acquired in retail drugstores and 14% were provided by Sistema Único de Saúde units (SUS - National Health System). These data point to the difficulty in accessing health units and the low drug coverage in Salvador.

All the 269 drugs with different commercial names used by children corresponded to 113 distinct active principles. Of these active principles, only 58.4% were included in the RENAME. Of all the products, 70 (26%) were inadequate for child use, reflecting the limited impact of ongoing pharmaceutical care policies on drug use cultural habits in Brazil.

The ten most used drugs comprised 54% of the total, with a predominance of analgesics/antipyretics, decongestants, iodide syrups, expectorants and mucolytics. In Sweden, where there is a strict control over drug commercialization, the ten most used drugs comprised 70% of the total, in a study performed with children.1

Analgesics/antipyretics are frequently used in children, probably due to the fact that fever is a common manifestation in childhood, in addition to the use of this class of over-the-counter drugs becoming ordinary. On the other hand, the use of systemic antibiotics for cough and flu/cold is also frequent, although rarely justifiable, given the viral etiology of the majority of these infections. However, the use of decongestants, expectorants and mucolytics is less and less recommended, once they expose children to risks without offering an equivalent benefit.18,19

After adjustment, there was no association between overall drug use and socioeconomic variables, except for maternal ethnicity. In terms of ethnicity, children of black mothers used 13% (PR = 0.87) less drugs than children of white mothers. When controlling for socioeconomic variables and health status, this value rose to 15% (PR = 0.85). This result may indicate that there are ethnic differences in this study which are not explained by socioeconomic variables. In this case, these variables are probably associated with use of services and access to drugs. A study performed in the United States found ethnic and racial differences in the use of drugs prescribed for children and which remained in the multivariate analysis adjusted for health status and use of services.13

As regards maternal level of education, researchers found higher drug use prevalences in children whose mothers had nine of more years of study. However, level of education was not significant in the crude analysis or that adjusted for confounding variables. Mothers with higher level of education would have greater awareness of drug use in their children because they had more access to information and health services. In addition, Sanz et al21 did not find differences in level of education in Spain.

Studies performed in developed and developing countries have revealed that drug use is associated with the presence of chronic diseases or conditions.2,6,11,12 In the present study, the presence of chronic diseases/conditions was positively and significantly associated with drug use in the crude analysis, but not statistically significant in the adjusted analysis. Health status indicators (worse health perception reported by the mother and interruption of activities/school absence due to health problems in the last two weeks) showed positive and significant association in the non-adjusted model and after adjustment for confounding variables.

The present study showed association between a higher number of medical consultations and drug use, findings that are in agreement with those of other studies in Brazil.2,5,6,26 Medical consultations converted into prescriptions may indicate deficiencies in the professional qualification system, difficulties and limitations related to conditions for adequate professional practice.26

Despite the use of logistic regression in cross-sectional studies with binary outcomes, Poisson regression was selected as it directly estimates prevalence ratios. It is known that the use of odds ratio as risk estimate for outcomes with high prevalence results in overestimation, thus hindering the interpretation of results.4

Some limitations to the present study must be considered. The household survey is subject to bias from interviewers and interviewees, which cannot always be controlled. The survey of reasons for drug use according to medical recommendation was not conducted due to operational difficulties, and only information reported by the mothers was used. Moreover, the period when data collection was performed, from February to May 2006, coincided with the local rainy season, when there was an increase in the incidence of viral diseases and dengue cases, which may have contributed to greater use of certain classes of drugs, such as analgesics, antipyretics, anti-cough drugs, expectorants, mucolytics and anti-asthma drugs. In the present study, some procedures were adopted to minimize memory bias, including the 15-day recall period to assess drug use in children, data collection standardization, and request for package and/or prescription of drugs used.

In conclusion, children aged between four and 11 years are usually in a stage of life when health problems justifying drug use are not frequent. Drug use, in addition to being an important indicator of health problems, also reflects social inequalities, health system deficiencies and qualities, the country's drug regulation, the medical education, cultural habits and the pharmaceutical market composition, among other factors. Results from the present study point to deficiencies in the SUS coverage in the city of Salvador, as well as inadequate population access to drugs in health units, particularly among poorer individuals. In turn, the profile and factors associated with drug use indicate which groups would be more subject to excessive use, in addition to aspects that are subject to intervention, thus contributing to rational drug use promotion strategies.

REFERENCES

• Correspondence:
Djanilson Barbosa dos Santos
Centro de Ciências da Saúde,
Universidade Federal do Recôncavo da Bahia
R. do Cajueiro, s/n
44570-000 Santo Antônio de Jesus, BA, Brasil
E-mail:

Revised: 4/4/2009

Approved: 17/4/2009

Article based on doctoral thesis by Santos DB, presented to the Programa de Pós-Graduação em Saúde Coletiva, Instituto de Saúde Coletiva, Universidade Federal da Bahia (Bahia Federal University Institute of Collective Health Postgraduate Program in Collective Health), in 2008.

• a
World Health Organization. WHO Collaborating Centre for Drug Statistics Methodology [internet]. Oslo; 2001[cited 2008 May 01]. Available from:
• b
Ministério da Saúde. Departamento de Assistência Farmacêutica e Insumos Estratégicos. Relação nacional de medicamentos. 4. ed. Brasília; 2007.
• 1. Al-Windi A, Elmfeldt D, Svärdsudd K. Determinants of drug utilization in a Swedish municipality. Pharmacoepidemiol Drug Saf. 2004;13(2):97-103. DOI: 10.1002/pds.864
• 2. Arrais PS, Brito LL, Barreto ML, Coelho HL. Prevalência e fatores determinantes do consumo de medicamentos no Município de Fortaleza, Ceará, Brasil. Cad Saude Publica. 2005;21(6):1737-46. DOI: 10.1590/S0102-311X2005000600021
• 3. Barreto ML, Cunha SS, Alcântara-Neves N, Carvalho LP, Cruz AA, Stein RT, et al. Risk factors and immunological pathways for asthma and other allergic diseases in children: background and methodology of a longitudinal study in a large urban center in Northeastern Brazil (Salvador-SCAALA study). BMC Pulm Med. 2006;6:1-15. DOI: 10.1186/1471-2466-6-15
• 4. Barros AJ, Hirakata VN. Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio. BMC Med Res Methodol. 2003;3:1-13. DOI: 10.1186/1471-2288-3-21
• 5. Beria JU, Victora CG, Barros FC, Teixeira AB, Lombardi C. Epidemiologia do consumo de medicamentos em crianças de centro urbano da região sul do Brasil. Rev Saude Publica. 1993;27(2):95-104. DOI: 10.1590/S0034-89101993000200004
• 6. Bertoldi AD, Barros AJ, Hallal PC, Lima RC. Utilização de medicamentos em adultos: prevalência e determinantes individuais. Rev Saude Publica. 2004;38(2):228-38. DOI: 10.1590/S0034-89102004000200012
• 7. Bonati M. Epidemiologic evaluation of drug use in children. J Clin Pharmacol. 1994;34(4):300-5.
• 8. Bricks LF, Leone C. Utilização de medicamentos por crianças atendidas em creches. Rev Saude Publica. 1996;30(6):527-35. DOI: 10.1590/S0034-89101996000600006
• 9. Cesar JA, Mendoza-Sassi R, Horta BL, Ribeiro PR, D´Avila AC, Santos FM, et al. Indicadores básicos de saúde infantil em área urbana no extremo sul do Brasil: estimando prevalências e avaliando diferenciais. J Pediatr (Rio J). 2006;82(6):437-44. DOI: 10.2223/JPED.1550
• 10. Ciofi degli Atti ML, Massari M, Bella A, Boccia D, Filia A, Salmaso S, et al. Clinical, social and relational determinants of paediatric ambulatory drug prescriptions due to respiratory tract infections in Italy. Eur J Clin Pharmacol. 2006;62(12):1055-64. DOI: 10.1007/s00228-006-0198-8
• 11. Eggen AE. Pattern of drug use in a general population-prevalence and predicting factors: the Tromso study. Int J Epidemiol. 1994;23(6):1262-72. DOI: 10.1093/ije/23.6.1262
• 12. Eggen AE. Patterns of medicine use in a general population (0-80 years). The Influence of age, gender, diseases and place of residence on drug use in Norway. Pharmacoepidemiol Drug Saf. 1997;6(3):179-87. DOI:10.1002/(SICI)1099-1557(199705)6:3<179::AID-PDS258>3.0.CO;2-P
• 13. Hahn BA. Children's health: racial and ethnic differences in the use of prescription medications. Pediatrics 1995;95(5):727-32.
• 14. Headley J, Northstone K. Medication administered to children from 0 to 7.5 years in the Avon Longitudinal Study of Parents and Children (ALSPAC). Eur J Clin Pharmacol. 2007;63(2):189-95. DOI: 10.1007/s00228-006-0231-y
• 15. Kogan MD, Pappas G, Yu SM, Kotelchuck M. Over-the-counter medication use among US preschool-age children. JAMA 1994;272(13):1025-30. DOI: 10.1001/jama.272.13.1025
• 16. Kovar MG. Use of medications and vitamin-mineral supplements by children and youths. Public Health Rep. 1985;100(5):470-3.
• 17. Laporte JR, Porta M, Capella D. Drug utilization studies: a tool for determining the effectiveness of drug use. Br J Clin Pharmacol. 1983;16(3):301-4.
• 18. Mallol J, Sole D, Asher I, Clayton T, Stein R, Soto-Quiroz M, et al. Prevalence of asthma symptoms in Latin America: the International Study of Asthma and Allergies in Childhood (ISAAC). Pediatr Pulmonol. 2000;30(6):439-44. DOI: 10.1002/1099-0496(200012)30:6<439::AID-PPUL1>3.0.CO;2-E.
• 19. Pratter MR. Cough and the common cold: ACCP evidence-based clinical practice guidelines. Chest 2006;129(1 Suppl):72-4. DOI: 10.1378/chest.129.1_suppl.72S
• 20. Rajmil L, Ruiz C, Segu JL, Fernandez E, Segura A. Factores asociados al consumo de medicamentos en la población infantil. Med Clin (Barc). 2000;114(6):214-6.
• 21. Sanz EJ. Drug prescribing for children in general practice. Acta Paediatr. 1998;87(5):489-90. DOI: 10.1080/08035259850158155
• 22. Schirm E, van den Berg P, Gebben H, Sauer P, De Jong-van den Berg L. Drug use of children in the community assessed through pharmacy dispensing data. Br J Clin Pharmacol. 2000;50(5):473-8. DOI: 10.1046/j.1365-2125.2000.00275.x
• 23. Soumerai SB, Ross-Degnan D. Drug prescribing in pediatrics: challenges for quality improvement. Pediatrics 1990;86(5):782-4.
• 24. Stephenson T. The medicines for children agenda in the UK. Br J Clin Pharmacol. 2006;61(6):716-9. DOI: 10.1111/j.1365-2125.2006.02676.x
• 25. Strina A, Cairncross S, Barreto ML, Larrea C, Prado MS. Childhood diarrhea and observed hygiene behavior in Salvador, Brazil. Am J Epidemiol. 2003;157(11): 1032-8. DOI: 10.1093/aje/kwg075
• 26. Weiderpass E, Beria JU, Barros FC, Victora CG, Tomasi E, Halpern R. et al. Epidemiologia do consumo de medicamentos no primeiro trimestre de vida em centro urbano do Sul do Brasil. Rev Saude Publica 1998;32(4):335-44. DOI: 10.1590/S0034-89101998000400005
Correspondence: Djanilson Barbosa dos Santos Centro de Ciências da Saúde, Universidade Federal do Recôncavo da Bahia R. do Cajueiro, s/n 44570-000 Santo Antônio de Jesus, BA, Brasil E-mail: dejab@bol.com.br a World Health Organization. WHO Collaborating Centre for Drug Statistics Methodology [internet]. Oslo; 2001[cited 2008 May 01]. Available from: http://www.whocc.no b Ministério da Saúde. Departamento de Assistência Farmacêutica e Insumos Estratégicos. Relação nacional de medicamentos. 4. ed. Brasília; 2007.

# Publication Dates

• Publication in this collection
20 Oct 2009
• Date of issue
Oct 2009

# History

• Accepted
17 Apr 2009
• Reviewed
04 Apr 2009


text:
# Coefficients of Product of Two Polynomials

## Theorem

Let $R$ be a commutative ring with unity.

Let $f, g \in R \sqbrk x$ be polynomials over $R$.

For a natural number $n \ge 0$, let:

$a_n$ be the coefficient of the monomial $x^n$ in $f$.
$b_n$ be the coefficient of the monomial $x^n$ in $g$.

### As an indexed summation

The coefficient $c_n$ of $x^n$ in $f g$ is the sum:

$c_n = \displaystyle \sum_{k \mathop = 0}^n a_k b_{n - k}$

### As an indexed summation bounded by degrees

Let $\deg f$ and $\deg g$ be their degrees.

The coefficient $c_n$ of $x^n$ in $fg$ is the sum:

$c_n = \displaystyle \sum_{k \mathop = n - \deg g}^{\deg f} a_k b_{n - k}$


text:
CA$2.00 What is the difference between expressions and equations? What does it mean “to solve an equation”? The answers to the above questions are provided in this lesson. An equation is an equality of two quantities and it always contains an equal sign. To solve an equation means to determine the value of the unknown(s) that makes the equation true, so that when the unknown is being substituted with the value in the equation, the left side is equal the right side. An expression does not have an equal sign, but it may contain variables that represent a certain quantity or relationship. To simplify an expression means to complete operations withing the expression that would bring it to its simplest form. In order to do that collecting like terms ins required. Like terms are terms that have different coefficients but identical variables with the same exponent. Grade 7 Workbook (22 pages with answers) CA$4.00

You are going to learn how to solve a linear equation by completing the reverse BEDMAS and performing opposite operations. For example, an equation 2x + 3 = 9 could be solved by first subtracting 3 from both sides of the equation and then dividing both sides of the equation by 2. Thus, x = 3. It is important to make sure that the same operation is done to both sides of the equation to keep the equation balanced.

Collecting like terms is often necessary on one or both sides of the equation.

Doing the “left side, right side check” is an important component of solving equations, as it would help you determine whether the solution is correct. This lesson will teach you how to do it.

#### Grade 7 Like Terms and Equations Quiz

Collect like terms: 2a − 7a + 3a
Collect like terms: 8x + 5y − 3x − 9y + 10
Solve an equation: 3x = 0.27
Solve an equation: 3 + x = −4.5
Solve an equation: 8x − 4x = 16
Solve an equation: 7x + 2 = 22 − 3x


text: Ji-Hwan Jung Post-Doc Sungkyunkwan University jh56k@skku.edu History SRC Post-doc, Applied Algebra and Optimization Research Center, Sungkyunkwan University, September 2017 - Current Post-doc in Sungkyunkwan University, September 2016 - August 2017 Post-doc in Mathematics, Institute of Basic Science, Sungkyunkwan University, June 2016 - August 2016 Sungkyunkwan University Post Doc in BK21+, June 2015 - May 2016 Sungkyunkwan University Ph.D. in Mathematics, September 2014 - April 2015 Sungkyunkwan University M.S. in Mathematics, 2009 Gyeongsang National University B.S. in Mathematics, 2006 Research Interests Riordan group theory, q-theory, Enumerative combinatorics, Orthogonal polynomials. Publications Horizontal and vertical formulas for exponential Riordan matrices and their applications (with G.-S. Cheon, P. Barry), Linear Algebra Appl. 541 (2018), 266-284. The r-Bessel and Restricted r-Bell Numbers (with I. Mezo, J. L. Ramirez), Australasian Journal of Combinatorics, 70 (2018), 202-220. The $q$-Sheffer sequences of a new type and associated orthogonal polynomials (with G.-S. Cheon), Linear Algebra Appl. 491 (2016), 171-186. Some combinatorial applications of the q-Riordan matrix (with G.-S. Cheon), Linear Algebra Appl. 482 (2015), 241-260. A q-analogue of the Riordan group (with G.-S. Cheon and Y. Lim), Linear Algebra and its Applications, 439 (2013), 4119-4129 Generalized Bessel numbers and some combinatorial settings (with G.-S. Cheon and L. W. Shapiro), Discrete Mathematics, 313 (2013), 2127-2138 $r$-Whitney numbers of Dowling lattices (with G.-S. Cheon), Discrete Mathematics, 312 (2012), 2337-2348.


text:
# setup-py-generation

Options to control how setup.py is generated from a `python_distribution` target.

Config section: `[setup-py-generation]`

## Basic options

### `first_party_dependency_version_scheme`

`--setup-py-generation-first-party-dependency-version-scheme=<FirstPartyDependencyVersionScheme>`
`PANTS_SETUP_PY_GENERATION_FIRST_PARTY_DEPENDENCY_VERSION_SCHEME`
one of: `exact, compatible, any`
default: `exact`

What version to set in `install_requires` when a `python_distribution` depends on other `python_distribution`s. If `exact`, will use `==`. If `compatible`, will use `~=`. If `any`, will leave off the version. See https://www.python.org/dev/peps/pep-0440/#version-specifiers.


text:
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# Have you received a Fall 2020 Scholarship?

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Have you received a Fall 2020 Scholarship?

We have been getting a lot of parents reaching out about this issue ... and to date we are unaware of any parents receiving scholarships ... so we wanted to ask. Have your received a Fall 2020 Scholarship?
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# $31,999 Raised in October – WORST MONTH YET!!! Published on OCTOBER FUNDRAISING – WORST YET –$31,999:  Friends … October was the worst fundraising month yet for the (not so) Exceptional SC Board.  Worse than even January 2020 … BEFORE they were even open / accepting donations.

October 2020 Fundraising: $31,999.00 =$1,032.23 / day

Below for your reference are the results from 2019.  It does not take a rocket scientist to conclude this is going to be a disaster … AGAIN.

The (not so) Exceptional SC Board cost children $7.45 MILLION in 2019 … it now appears the (not so) Exceptional SC Board will cost children$10 MILLION +/- in 2020.

We call that … Board malpractice!!!

So why won’t they PUT THE KIDS FIRST?!?!?!?

So where is (not so) Exceptional SC:  Well … the (not so) Exceptional SC Board sent a few email blasts to parents and school officials back in September … after Chad Connelly was fired … pushing for the legislature to INCREASE THEIR FEES … clearly reflecting their priorities (#FollowTheMoney!!!),
… so we know the (not so) Exceptional SC Board knows “how” to send email updates.
So why then has the (not so) Exceptional SC Board gone silent …. again???

DON’T LET THE (NOT SO) EXCEPTIONAL SC BOARD OFF THE HOOK!!!  CALL THEM!!!

They asked for (or offered to do) the JOB.  So make them!!!

HOW CAN YOU HELP?:

PLEASE – Contact the EXCEPTIONAL SC BOARD:

• Ask them if they will support INDEPENDENT NON-PROFITS
• Ask them if they will meet to discuss a solution.
• Tell them they are killing the program.
• Let them know what this is doing to your family.
• It is not hard … but the time for them to speak-up is YESTERDAY!!!

Betsy Fanning
843-884-7046 x111 (school)

Michael Acquilano, JD
Charleston Diocese
MAcquilano@catholic-doc.org
843-261-0535 (office)
843-709-2717 (cell)

Edward Earwood
Executive Director
SC Association of Christian Schools
eearwood@christianeducation.org
803-798-7558 (office)
843-513-5010 (cell)

Dr. Spencer Jordan
Executive Director
SC Association of Independent Schools
803-535-4820 (office)

# Senator Vince Sheheen – GONE!!!

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We have talked with A LOT of parents and friends in Senator Vincent Sheheen’s district (D – Camden) over the past few years … exposing his opposition to the K-12 tax credit program … and NOBODY was happy about what he has been doing to our kids … what he was doing to YOUR KIDS!!!

As you all know … Senator Sheheen lead the charge to KILL THIS PROGRAM!!!

Senator Sheheen is also the one who called Governor Nikki Halley a “whore” back in 2014 … but that is a different story about Senator Sheheen … just indicative of “who” he really is.

As for our program … as recently as September 23rd, 2020 … during the middle of a pandemic …  Senator Sheheen KILLED the SC House Amendment to help with a few minor tweaks.  Nothing big … just minor tweaks.  What arrogance!!!

Well … it cost him re-election … and now, one of the MOST POWERFUL legislators in the SC Senate is GONE!!!

Will someone else step up to be “the voice” of the opposition to kill fixing this program?  Maybe … but we think they would be crazy to do so … so we shall have to wait and see.  We will however be ready!!!

THANK YOU PENRY GUSTAFSON … our “new” SC State Senator from Camden.  Penry is a good friend and we fully expect will be a HUGE supporter of this program and YOUR KIDS!!!

# Governor Asks SC Supreme Court to Reconsider

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Well, for now … they are going to keep trying to FORCE the “failed” Government Run Education Savings Account (ESA or GRESA) process.

Don’t let the article title fool you.  Yes, it is the US Attorney for the State of South Carolina that has filed the brief … but “who” is the US Attorney for SC?

Peter McCoy is our US Attorney.

Peter is good guy for all we know … we have no problems with him … but he was most recently a member of the SC House of Representatives.

And for some reason … HE DID NOT sponsor H 3202 / S 131 (the tax credit scholarship bill) … we did not push hard … and we guess due to the LIES spread by the “paid” advocates …

… but he did sponsor the “paid” advocates ESA / GRESA bill (H 3681 / S 523 / S 556) that has been a total disaster …

… and then Representative Peter McCoy WITHDREW HIS SPONSORSHIP when he realized what a political disaster this ESA / GRESA bill was.

All those representatives and more got off that ESA / GRESA bill right after they had two hearings on it in the HOUSE.  We were there … it was a total mess.

So … don’t be fooled by the ongoing efforts to push through the ESA / GRESA … we don’t think it is going anywhere.

Perhaps we need to REMIND the Governor’s Office that we have a 100% LEGAL, bulletproof, and PROVEN solution …

K-12 TAX CREDIT SCHOLARSHIPS run by IDEPENDENT NON-PROFITS!


text:
what will be the events relative to the ground observer , a time-like or space like?

Tags: events, ground, observer, relative, space, timelike
 P: 163 Please refer to the attached diagram The train moves in the direction B-A If the events seen in the ground observer simultaneously, it should be seen at A before B in the train In special case, the difference in times between A and B according to the train observer could be equal to the time a light signal takes to travel from A to B only if v/c=0.618 However, if the light travel from A to B relative to the train observer, it should do so relative to the ground one as well. But because of the experiment setup, still the ground observer sees the 2 events happen at the same time So what will be the events relative to the ground observer, a time-like or space like? Thanks,,, http://www.physicsforums.com/attachm...1&d=1330188385 Attached Thumbnails
 P: 163 any answer to my question!
 P: 1,098 seperated spatialy and can be observed as happening simultaniously, spacelike I think.
P: 132

what will be the events relative to the ground observer , a time-like or space like?

If two separate events are simultaneous in a particular frame, they have a space-like separation in all frames.
 P: 1,098 Good point the distinction between spacelike & timelike is invariant.
P: 163
 Quote by Michael C If two separate events are simultaneous in a particular frame, they have a space-like separation in all frames.
OK,,, but according to my calculation attached here, the Δt between A and B for the train observer can be equal to the Δttaken by a light signal from A to B in case of v/c=0.618. This yields a time-like separation !
 Emeritus Sci Advisor PF Gold P: 9,014 In the first sentence (in the attachment), you're talking about A and B as if they are events. Later you're talking about them as if they are locations in space (specifically in the slice of spacetime that the ground considers space). This makes your argument quite confusing. If A and B are events, it only makes sense to say that a light signal is sent from A to B if their separation is lightlike, but this would of course immediately contradict the earlier claim that there's an inertial frame in which A and B are simultaneous. Then you start talking about calculating the time it takes the signal to go from A to B. By then you are clearly thinking of A and B as locations, not events. The signal would be sent from an event E on A's world line and received at an event F on B's world line. The separation between E and F is obviously lightlike.
 P: 249 The ground observer will see the two "simultanious" events happen at two different times, this is because it will take longer for light to reach the ground observer, but this would only be an illusion since the photon would only be traveling a larger distance from one of the points. Similiar to how we look back in time when we look at the stars, the stars are not younger just because we see them that way. It just takes a certain amount of time for the light to reach the observer since it travels at a limited speed. So then, I would say the seperation of the events is just space like.
Emeritus
PF Gold
P: 9,014
 Quote by John232 The ground observer will see the two "simultanious" events happen at two different times, this is because it will take longer for light to reach the ground observer,
It has nothing to do with that. When we're talking about what someone "sees" or "experiences", we're not talking about what their eyes or video cameras would pick up. We're talking about the coordinate assignments they would make. An observer on the ground "sees" two events as simultaneous if and only if he assigns the same time coordinate to them.
P: 1,098
 Quote by John232 The ground observer will see the two "simultanious" events happen at two different times, this is because it will take longer for light to reach the ground observer, but this would only be an illusion since the photon would only be traveling a larger distance from one of the points. Similiar to how we look back in time when we look at the stars, the stars are not younger just because we see them that way. It just takes a certain amount of time for the light to reach the observer since it travels at a limited speed. So then, I would say the seperation of the events is just space like.
I disagree with that, I can use my head and consider the time that the light has travelled an deduce the star is now older, but from an observed "my reality" perspective what's measureable is all of the information I have ( or could possibly have) regarding that "distant star". The physical reality travels at c. all else is "elsewhere" and sometimes termed unphysical.

That being said, the star is actually "younger" here compared to over "there". not an illusion, a reality. Said differently, at the location here the "distant star" is not old yet, because of the spatial separation more time needs to pass until the star is "old" over here. It would be a safe bet the star is even older over there but that proof does not exist over here, it is not a "reality" here, more an "illusion" of the "mind's eye", specifically an assumption. ( of course physics can predict this future accurately, calculating the age of the star over there, and intuitively is reffered to as "it's age", but comparatively thats relative)

(mumbo jumbo here, but I think it could even be physicaly possible for there to be a "closed timelike curve" (or spacelike? idk) that "transports" the light to the observer location faster than light years)
P: 163
 Quote by Fredrik In the first sentence (in the attachment), you're talking about A and B as if they are events. Later you're talking about them as if they are locations in space (specifically in the slice of spacetime that the ground considers space). This makes your argument quite confusing. If A and B are events, it only makes sense to say that a light signal is sent from A to B if their separation is lightlike, but this would of course immediately contradict the earlier claim that there's an inertial frame in which A and B are simultaneous. Then you start talking about calculating the time it takes the signal to go from A to B. By then you are clearly thinking of A and B as locations, not events. The signal would be sent from an event E on A's world line and received at an event F on B's world line. The separation between E and F is obviously lightlike.
I meant A and B as events

If A and B are simultaneous for the ground observer, they must have a spacelike separation for the train observer. This should not permit Δt to be long enough to allow B receiving any light from A. But that may happen if v/c=0.618 !
Emeritus
PF Gold
P: 9,014
 Quote by Adel Makram I meant A and B as events
Then your calculation doesn't make much sense. You wrote "AB", meaning "the distance in space between A and B in the ground's(?) rest frame". That's OK, since A and B are by assumption simultaneous in that frame. But then you multiplied AB by ##1/\gamma##, expecting to get the distance in space between A and B in the other frame. The concept of distance in space in the train's frame between A and B doesn't make sense, since A and B aren't simultaneous in that frame. What you're calculating this way is the distance in the train's frame between the two points on the ground where A and B occurred. This is not a distance between A and B. It's the distance in the train's frame between A and and an event C on the world line of the point on the ground where B occurred. C would occur significantly later than B, but still not late enough to receive a light signal from A.
P: 163
 Quote by Fredrik Then your calculation doesn't make much sense. You wrote "AB", meaning "the distance in space between A and B in the ground's(?) rest frame". That's OK, since A and B are by assumption simultaneous in that frame. But then you multiplied AB by ##1/\gamma##, expecting to get the distance in space between A and B in the other frame. The concept of distance in space in the train's frame between A and B doesn't make sense, since A and B aren't simultaneous in that frame. What you're calculating this way is the distance in the train's frame between the two points on the ground where A and B occurred. This is not a distance between A and B. It's the distance in the train's frame between A and and an event C on the world line of the point on the ground where B occurred. C would occur significantly later than B, but still not late enough to receive a light signal from A.
The distance AB for the train observer wont change because he sees the event A happens before B. He always considered A and B simultaneous whenever he measures AB as a distance.
The derivation of Δt according to LT is also based on that assumption and therefore multiplying AB by ##1/\gamma## to yield AB. So multiplication by ##1/\gamma## occurs on both sides of the equations i & ii and it will cancel each other out
And even if you dont want to consider ##1/\gamma##, no problem, as the quadratic equation still remains valid because AB will cancel each other out again
Emeritus
PF Gold
P: 9,014
 Quote by Adel Makram The distance AB for the train observer wont change because he sees the event A happens before B. ... So multiplication by ##1/\gamma## occurs on both sides of the equations i & ii and it will cancel each other out And even if you dont want to consider ##1/\gamma##, no problem, as the quadratic equation still remains valid because AB will cancel each other out again
I don't understand what you're saying here.

 Quote by Adel Makram The derivation of Δt according to LT is also based on that assumption and therefore multiplying AB by ##1/\gamma## to yield AB.
##(AB)/\gamma## isn't the distance between A and B in the train's frame. There's no such thing as a distance between A and B in the train's frame, because A and B are not simultaneous in that frame. ##(AB)/\gamma## is the distance in the train's frame between the points on the ground where events A and B occurred. It's a distance in spacetime along a simultaneity line of the train's frame. There's such a simultaneity line through A, and another one through B, but there's no such simultaneity line through both. So ##(AB)/\gamma## is definitely not the distance in the train's frame between A and B.

I think you need to think about what you're actually calculating using the length contraction formula. You can't plug in the distance between two events and expect to get the distance between those same events in another coordinate system. That's not just wrong, it doesn't make sense. Think about it this way instead: In a spacetime diagram where the axes are the t and x axes of the ground's frame, the world lines of the two points on the ground are vertical lines. A and B are two points on those two lines. Since they are simultaneous, there's a horizontal line that goes through both of them. The length of that line segment from B to A is what you called AB. But ##(AB)/\gamma## is the length that an observer on the train would assign to a line with slope 1/v between two events where such a line intersects the two vertical lines.
P: 132
 Quote by Adel Makram The distance AB for the train observer wont change because he sees the event A happens before B.
"Won't change" relative to what? The distance between the places where A and B happen will certainly be different when measured in different frames.

If you assign coordinates to the events A and B in the ground frame, you can use the Lorentz transformation to work out the coordinates in the train frame:

THE GROUND FRAME:
Let's say that the distance between the two events in the ground frame is d. To make things easy, we'll put event A at the origin:
Event A: t = 0, x = 0
Event B: t = 0, x = d.

THE TRAIN FRAME:
We define the train frame to have the same origin as the ground frame. It is moving relative to the ground frame along the x axis at a velocity of v. The Lorentz transformation gives us the coordinates of the two events in this frame:
Event A: t' = 0, x' = 0
Event B: t' = -$\gamma$vd/c$^{2}$, x' = $\gamma$d.

Increasing the velocity difference between the two frames will not only increase the time separation between A and B, it will also increase the spatial separation: you can see from the coordinates that the distance in space between the two events has been multiplied by $\gamma$. The space-time interval between A and B stays the same.
P: 249
 Quote by nitsuj I disagree with that, I can use my head and consider the time that the light has travelled an deduce the star is now older, but from an observed "my reality" perspective what's measureable is all of the information I have ( or could possibly have) regarding that "distant star". The physical reality travels at c. all else is "elsewhere" and sometimes termed unphysical.
This may just be too hippy for me. So, if I tied a string around Mars and then held the other side at Earth would their be a reality that exist at the speed of sound?

 Quote by Fredrik It has nothing to do with that. When we're talking about what someone "sees" or "experiences", we're not talking about what their eyes or video cameras would pick up.
Shouldn't these be the same two things?

 Quote by Michael C Increasing the velocity difference between the two frames will not only increase the time separation between A and B, it will also increase the spatial separation:
If A and B are not on the train then wouldn't the distance from A to B seen from on the train shorten, since A to B could be "seen" as a single object in motion relative to the train?
P: 132
 Quote by John232 If A and B are not on the train then wouldn't the distance from A to B seen from on the train shorten, since A to B could be "seen" as a single object in motion relative to the train?
A and B are not objects, they are events.

I'm not sure quite what you mean by saying that "A to B could be "seen" as a single object in motion relative to the train". Are you imagining that a single object could be present at both event A and event B? That won't work, since neither event falls within the light cone of the other.
Emeritus


text:
## routes_doubt

hi. as an experiment i decide to: rake routes , considering my routes.rb file has only: map.resources users. well, we all know the output, but based on this output the last 3 mappings which are: show(get), update(put) and destroy(delete):

user GET /users/:id {:action=>”show”, :controller=>”users”}
PUT /users/:id {:action=>”update”, :controller=>”users”}
DELETE /users/:id {:action=>”destroy”, :controller=>”users”}

based on the output above i decided to write the equivalent routes in the routes.rb file in order to mimic what map.resources does. so we will have 7 routes. to simplify let’s just consider here these last 3 routes. first, based on the output above, my conclusion is that i could use 3 routes with the same name: map.user and differentiate then with the :method symbol, being get, put and delete for each one of them … so rails would know which one to use based on the :method

map.user ‘users/:id’, … , :method => :get
map.user ‘users/:id’, … , :method => ut
map.user ‘users/:id’, … , :method => :delete

well, that doesn’t work … if i click delete in the view then the show action will be triggered. my 2nd conclusion is that since i’m not using map.resources and instead i’m using named_routes, then the routing system will use the top-first rule

my doubt is, how rails understand map.resources since the output from rake routes doesn’t imply us to do something like:

map.user_show ‘users/:id’, … , :method => :get
map.user_update ‘users/:id’, … , :method => ut
map.user_delete ‘users/:id’, … , :method => :delete

plus if i named_route like the sample above, i don’t need to specify which method to use, cause the routes are named. right?

then my 3rd conclusion is that rails should understand:

map.user ‘users/:id’, … , :method => :get
map.user ‘users/:id’, … , :method => ut
map.user ‘users/:id’, … , :method => :delete

based on the :method differentiation. i also did: :requirements => {:method => :delete} in routes.rb or user_path(user) in my view, but no success.


text:
Home > CCA2 > Chapter 12 > Lesson 12.1.3 > Problem12-46

12-46.

Graph. Homework Help ✎

1. $(-2, 3, -2)$

What does it mean if there are $3$ coordinates?
What does that tell you about the dimensions of the coordinate system?

1. $3x - 2y - 3z = -6$

Note that the triangle represents a plane.


text:
### 2.9.6 Working with ancient music—scenarios and solutions

Working with ancient music frequently involves particular tasks which differ considerably from the modern notation for which LilyPond is designed. In the rest of this section, a number of typical scenarios are outlined, with suggestions of solutions. These involve:

• how to make incipits (i.e. prefatory material to indicate what the original has looked like) to modern transcriptions of mensural music;
• how to achieve the Mensurstriche layout frequently used for modern transcriptions of polyphonic music;
• how to transcribe Gregorian chant in modern notation;
• how to generate both ancient and modern notation from the same source.

TBC

#### Mensurstriche layout

Mensurstriche (‘mensuration lines’) is the accepted term for bar lines that are drawn between the staves of a system but not through the staves themselves. It is a common way to preserve the rhythmic appearance of the original, i.e. not having to break syncopated notes at bar lines, while still providing the orientation aids that bar lines give.

The mensurstriche-layout where the bar lines do not show on the staves but between staves can be achieved with a StaffGroup instead of a ChoirStaff. The bar line on staves is blanked out by setting the transparent property.

global = {
\hide Staff.BarLine
s1 s
% the final bar line is not interrupted
\undo \hide Staff.BarLine
\bar "|."
}
\new StaffGroup \relative c'' {
<<
\new Staff { << \global { c1 c } >> }
\new Staff { << \global { c c } >> }
>>
}

#### Transcribing Gregorian chant

Gregorian chant can be transcribed into modern notation with a number of simple tweaks.

Stems. Stems can be left out altogether by \remove-ing the Stem_engraver from the Voice context:

\layout {
…
\context {
\Voice
\remove "Stem_engraver"
}
}

However, in some transcription styles, stems are used occasionally, for example to indicate the transition from a single-tone recitative to a fixed melodic gesture. In these cases, one can use either \hide Stem or \override Stem.length = #0 instead, and restore the stem when needed with the corresponding \once \override Stem.transparent = ##f (see example below).

Timing. For unmetered chant, there are several alternatives.

The Time_signature_engraver can be removed from the Staff context without any negative side effects. The alternative, to make it transparent, will leave an empty space in the score, since the invisible signature will still take up space.

In many cases, \set Score.timing = ##f will give good results. Another alternative is to use \cadenzaOn and \cadenzaOff.

To remove the bar lines, the radical approach is to \remove the Bar_engraver from the Staff context. Again, one may want to use \hide BarLine instead, if an occasional barline is wanted.

A common type of transcription is recitativic chant where the repeated notes are indicated with a single breve. The text to the recitation tone can be dealt with in two different ways: either set as a single, left-aligned syllable:

\include "gregorian.ly"
chant = \relative c' {
\clef "G_8"
c\breve c4 b4 a c2 c4  \divisioMaior
c\breve c4 c f, f \finalis
}

verba = \lyricmode {
\once \override LyricText.self-alignment-X = #-1
"Noctem quietam et" fi -- nem per -- fec -- tum
\once \override LyricText.self-alignment-X = #-1
"concedat nobis Dominus" om -- ni -- po -- tens.
}
\score {
\new Staff <<
\new Voice = "melody" \chant
\new Lyrics = "one" \lyricsto melody \verba
>>
\layout {
\context {
\Staff
\remove "Time_signature_engraver"
\remove "Bar_engraver"
\hide Stem
}
}
}

This works fine, as long as the text doesn’t span a line break. If that is the case, an alternative is to add hidden notes to the score, here in combination with changing stem visibility:

\include "gregorian.ly"
chant = \relative c' {
\clef "G_8"
\set Score.timing = ##f
c\breve \hide NoteHead  c c c c c
\override Stem.transparent = ##f \stemUp c4 b4 a
\hide Stem c2 c4  \divisioMaior
c\breve \hide NoteHead c c c c c c c
\undo \hide NoteHead c4 c f, f \finalis
}

verba = \lyricmode {
No -- ctem qui -- e -- tam et fi -- nem per -- fec -- tum
con -- ce -- dat no -- bis Do -- mi -- nus om -- ni -- po -- tens.
}

\score {
\new Staff <<
\new Voice = "melody" \chant
\new Lyrics \lyricsto "melody" \verba
>>
\layout {
\context {
\Staff
\remove "Time_signature_engraver"
\hide BarLine
\hide Stem
}
}
}

Another common situation is transcription of neumatic or melismatic chants, i.e. chants with a varying number of notes to each syllable. In this case, one would want to set the syllable groups clearly apart, usually also the subdivisions of a longer melisma. One way to achieve this is to use a fixed \time, e.g., 1/4, and let each syllable or note group fill one of these measures, with the help of tuplets or shorter durations. If the bar lines and all other rhythmical indications are made transparent, and the space around the bar lines is increased, this will give a fairly good representation in modern notation of the original.

To avoid that syllables of different width (such as “-ri” and “-rum”) spread the syllable note groups unevenly apart, the 'X-extent property of the LyricText object may be set to a fixed value. Another, more cumbersome way would be to add the syllables as \markup elements. If further adjustments are necessary, this can be easily done with s ‘notes’.

spiritus = \relative c' {
\time 1/4
\override Lyrics.LyricText.X-extent  = #'(0 . 3)
d4 \tuplet 3/2 { f8 a g } g a a4 g f8 e
d4 f8 g g8 d f g a g f4 g8 a a4  s
\tuplet 3/2 { g8 f d } e f g a g4
}

spirLyr = \lyricmode {
Spi -- ri -- _ _ tus  _ Do -- mi -- ni  _ re -- ple -- _ vit _
or -- _ bem _  ter -- ra -- _ rum, al -- _ _ le -- _ lu
-- _ ia.
}
\score {
\new Staff <<
\new Voice = "chant" \spiritus
\new Lyrics = "one" \lyricsto "chant" \spirLyr
>>
\layout {
\context {
\Staff
\remove "Time_signature_engraver"
\override BarLine.X-extent = #'(-1 . 1)
\hide Stem
\hide Beam
\hide BarLine
\hide TupletNumber
}
}
}

TBC

#### Editorial markings

Other languages: deutsch, español, français, italiano, 日本語.


text:
# zbMATH — the first resource for mathematics

Finite solvable groups with an irreducible character vanishing on just one class of elements. (English) Zbl 1127.20008
Let $$G$$ be a finite group. It is well-known that if $$\chi$$ is a nonlinear irreducible complex character of $$G$$, then $$\chi$$ vanishes on some conjugacy class of $$G$$. For solvable $$G$$, the author is interested in groups for which there exists a $$\chi$$ which vanishes on exactly one conjugacy class of $$G$$. The main result gives a detailed description of such groups (which is too technical to be reproduced in this review). He also classifies odd order groups which have an irreducible character vanishing on two classes.

##### MSC:
 20C15 Ordinary representations and characters 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks
Full Text:
##### References:
 [1] DOI: 10.1006/jabr.1996.0146 · Zbl 0860.20017 [2] Isaacs I. M., Character Theory of Finite Groups (1976) · Zbl 0337.20005 [3] DOI: 10.1081/AGB-200039286 · Zbl 1094.20013 [4] Zhmud E. M., Soviet Math. Dokl. 20 pp 795– (1979)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson

# Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set - Page 393: 26

#### Answer

$\dfrac{1}{x-1}$

#### Work Step by Step

Adding the numerators and copying the denominator, the given expression, $\dfrac{x-5}{x^2-4x+3}+\dfrac{2}{x^2-4x+3} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{x-5+2}{x^2-4x+3} \\\\= \dfrac{x-3}{x^2-4x+3} \\\\= \dfrac{x-3}{(x-3)(x-1)} \\\\= \dfrac{\cancel{x-3}}{(\cancel{x-3})(x-1)} \\\\= \dfrac{1}{x-1} .\end{array}

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
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 SIGMA: Year: Volume: Issue: Page: Find

 SIGMA, 2007, Volume 3, 039, 19 pages (Mi sigma165)

$N$-Wave Equations with Orthogonal Algebras: $\mathbb Z_2$ and $\mathbb Z_2\times\mathbb Z_2$ Reductions and Soliton Solutions

Vladimir S. Gerdjikova, Nikolay A. Kostovab, Tihomir I. Valcheva

a Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria
b Institute of Electronics, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria

Abstract: We consider $N$-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first $\mathbb Z_2$-reduction is the canonical one. We impose a second $\mathbb Z_2$-reduction and consider also the combined action of both reductions. For all three types of $N$-wave equations we construct the soliton solutions by appropriately modifying the Zakharov–Shabat dressing method. We also briefly discuss the different types of one-soliton solutions. Especially rich are the types of one-soliton solutions in the case when both reductions are applied. This is due to the fact that we have two diferent configurations of eigenvalues for the Lax operator $L$: doublets, which consist of pairs of purely imaginary eigenvalues, and quadruplets. Such situation is analogous to the one encountered in the sine-Gordon case, which allows two types of solitons: kinks and breathers. A new physical system, describing Stokes-anti Stokes Raman scattering is obtained. It is represented by a $4$-wave equation related to the $\mathbf B_2$ algebra with a canonical $\mathbb Z_2$ reduction.

Keywords: solitons; Hamiltonian systems

DOI: https://doi.org/10.3842/SIGMA.2007.039

Full text: PDF file (277 kB)
Full text: http://emis.mi.ras.ru/.../039
References: PDF file   HTML file

Bibliographic databases:

ArXiv: nlin.SI/0703002
MSC: 37K15; 17B70; 37K10; 17B80
Received: November 21, 2006; in final form February 8, 2007; Published online March 3, 2007
Language:

Citation: Vladimir S. Gerdjikov, Nikolay A. Kostov, Tihomir I. Valchev, “$N$-Wave Equations with Orthogonal Algebras: $\mathbb Z_2$ and $\mathbb Z_2\times\mathbb Z_2$ Reductions and Soliton Solutions”, SIGMA, 3 (2007), 039, 19 pp.

Citation in format AMSBIB
\Bibitem{GerKosVal07} \by Vladimir S.~Gerdjikov, Nikolay A.~Kostov, Tihomir I.~Valchev \paper $N$-Wave Equations with Orthogonal Algebras: $\mathbb Z_2$ and $\mathbb Z_2\times\mathbb Z_2$ Reductions and Soliton Solutions \jour SIGMA \yr 2007 \vol 3 \papernumber 039 \totalpages 19 \mathnet{http://mi.mathnet.ru/sigma165} \crossref{https://doi.org/10.3842/SIGMA.2007.039} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2299840} \zmath{https://zbmath.org/?q=an:1134.37028} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000207065200039} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889235929}

• http://mi.mathnet.ru/eng/sigma165
• http://mi.mathnet.ru/eng/sigma/v3/p39

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Gerdjikov, VS, “On classification of soliton solutions of multicomponent nonlinear evolution equations”, Journal of Physics A-Mathematical and Theoretical, 41:31 (2008), 315213
2. Gerdjikov V.S., Vilasi G., and Yanovski AB,, “The Inverse Scattering Problem for the Zakharov–Shabat System”, Lecture Notes in Physics, 748, 2008, 97–132
3. Gerdjikov V.S., Vilasi G., and Yanovski AB,, “The Lax Representation and the AKNS Approach”, Lecture Notes in Physics, 748, 2008, 37–70
4. Lombardo S., Sanders J.A., “On the classification of automorphic Lie algebras.”, Communications in Mathematical Physics, 299:3 (2010), 793-824
5. Gerdjikov V.S., Ivanov R.I., Kyuldjiev A.V., “On the N-wave equations and soliton interactions in two and three dimensions”, Wave Motion, 48:8 (2011), 791–804
6. Gerdjikov V.S., “On New Types of Integrable 4-Wave Interactions”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1487, ed. Todorov M., Amer Inst Physics, 2012, 272–279
7. V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, “The $N$-wave equations with $\mathcal{PT}$ symmetry”, Theoret. and Math. Phys., 188:3 (2016), 1305–1321
8. Gerdjikov V.S., “On Nonlocal Models of Kulish-Sklyanin Type and Generalized Fourier Transforms”, Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence, 681, eds. Georgiev K., Todorov M., Georgiev I., Springer International Publishing Ag, 2017, 37–52
9. G. G. Grahovski, A. J. Mustafa, H. Susanto, “Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces”, Theoret. and Math. Phys., 197:1 (2018), 1430–1450
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# ASTM International - ASTM D4530-00

## Standard Test Method for Determination of Carbon Residue (Micro Method)

inactive
 Organization: ASTM International Publication Date: 10 May 2000 Status: inactive Page Count: 6 ICS Code (Petroleum products in general): 75.080
##### scope:

1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to provide some indication of the relative coke forming tendency of such materials.

1.2 The test results are equivalent to the Conradson Carbon Residue test (Test Method D189).

Note 1-This procedure is a modification of the original method and apparatus for carbon residue of petroleum materials, where it has been demonstrated that thermogravimetry is another applicable technique. However it is the responsibility of the operator to establish operating conditions to obtain equivalent results when using thermogravimetry.

1.3 This test method is applicable to petroleum products that partially decompose on distillation at atmospheric pressure and was tested for carbon residue values of 0.10 to 30% (m/m). Samples expected to be below 0.10 weight% residue should be distilled to remove 90% (V/V) of the flask charge (see Section 9). The 10% bottoms remaining is then tested for carbon residue by this test method.

1.4 Ash-forming constituents as defined by Test Method D482, or non-volatile additives present in the sample will add to the carbon residue value and be included as part of the total carbon residue value reported.

1.5 Also in diesel fuel the presence of alkyl nitrates, such as amyl nitrate, hexyl nitrate or octyl nitrate, causes a higher carbon residue value than observed in untreated fuel, which may lead to erroneous conclusions as to the coke-forming propensity of the fuel. The presence of alkyl nitrate in the fuel may be detected by Test Method D4046.

1.6 The values stated in SI unites are to be regarded as the standard. The values given in parentheses are for information only.

1.7 This standard does not purport to address all of the safety problems, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety practices and to determine the applicability of regulatory limitations prior to use. For specific hazard statements see 8.2.3 and 8.4.

### Document History

May 1, 2020
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
June 1, 2015
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
May 15, 2011
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
November 1, 2007
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
January 1, 2006
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 0) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
January 1, 2006
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
May 10, 2003
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...
ASTM D4530-00
May 10, 2000
Standard Test Method for Determination of Carbon Residue (Micro Method)
1.1 This test method covers the determination of the amount of carbon residue (see Note 1) formed after evaporation and pyrolysis of petroleum materials under certain conditions and is intended to...


text:
In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2. It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups. The most important class of graded quadratic algebras is Koszul algebras.

## Definition

A graded quadratic algebra A is determined by a vector space of generators V = A1 and a subspace of homogeneous quadratic relations SVV (Polishchuk & Positselski 2005, p. 6). Thus

${\displaystyle A=T(V)/\langle S\rangle }$

and inherits its grading from the tensor algebra T(V).

If the subspace of relations is instead allowed to also contain inhomogeneous degree 2 elements, i.e. SkV ⊕ (VV), this construction results in a filtered quadratic algebra.