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In this article, the authors present explicit expressions for the series of sine and cosine products. The objective of the article is to provide a more general identity than the existing basic formula and offer explicit expressions for these series. Similar series with cosine products are studied and the Bernoulli and Euler polynomials are mentioned, which are particular cases of the Appell polynomials. The text uses mathematical formulas and proofs to support the presented results. Different cases are analyzed for specific values of n and basic identities are demonstrated. A series of mathematical formulas related to the sum of sine and cosine products is also presented, and multinomial coefficients are mentioned. The text is technical and focuses on specific mathematical aspects. [Extracted from the article]

Copyright of Revista Góndola, Enseñanza y Aprendizaje de las Ciencias is the property of Gondola, Ensenanza y Aprendizaje de las Ciencias and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article presents an analysis of the methodology for the calculation of environmental fines ordered in Article 40 of Law 1333 of 2009, developed by Article 11 of Decree 3678 of 2010 and Resolution 2086 of the same year, by identifying margins of technical discretion that can be seen in the variables that make up the mathematical formulas adopted therein and makes an approach to the discussion on the limits to such discretion, the tensions that in the specific case it generates with the principles of proportionality and equality and judicial control. [ABSTRACT FROM AUTHOR]

The article presents a new perspective on calorie consumption in running/walking. It analyzes the physical kinetics of this practice and develops a mathematical formula to calculate the mechanical energy consumed based on different parameters such as weight, distance covered, and runner's speed. It differentiates between walking and running, as during walking there must always be one foot in contact with the ground, while during running there is a small jump with each stride. The article presents the calculation of energy consumed based on the basic principles of the physical kinetics of a mobile object. It concludes that the energy consumed is proportional to the square of the speed and the distance covered. It also mentions the effect of body elevation with each stride in running, which consumes additional energy. This article presents a calculation of the mechanical energy consumed in walking and/or running, valid for both casual walkers and professional athletes. It highlights the popularity of this sport in today's society, associated with reducing body fat and maintaining muscle capacity. Additionally, a didactic strategy based on surprising physical phenomena is proposed to increase the appeal of physics and awaken students' curiosity. [Extracted from the article]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Livestock in semi-arid areas such as the province of Santa Elena has ancestral management with deficiencies in animal nutrition, which economically affects small farmers or livestock producers, especially in the dry season. This type of production is not considered a profitable business, but rather as a subsistence activity. Feeding problems and incipient handling of the animals prevent them from gaining weight for meat or producing more milk. The objective of this research was to predict the daily production of meat and milk in cattle from energy estimates of forage species using mathematical formulas, to estimate the necessary amount of fresh forage (kg) that is needed to cover the total energy requirements of the animal. The results of the bromatological analysis in the specific conditions of the province of Santa Elena determined the tree species Caesalpinia glabatra with the highest% of dry matter, Leucaena leucocephala and Moringa oleifera with the highest protein values. The energy value calculated for Moringa oleifera, Leucaena leucocephala and Caesalpinia glabatra presented moringa as the species that contributes the highest energy value to cattle. The energy estimates that fresh forage and dry matter produce in catle, for Moringa oleifera, the highest amount of kg/meat/day and the highest amount of l/milk/day. The Caesalpinia glabatra species proved to be the forage species with the highest yield and animal load in adult bovine units per hectare. [ABSTRACT FROM AUTHOR]

In the face of the coronavirus disease 2019 (COVID-19) pandemic, the entire world is concerned with achieving desired herd immunity to overcome the current health crisis. Estimating the efficacy that could be attained in a population by combining vaccines of different brands or technologies would be a valuable asset for public health decision-makers in the present pandemic and in similar future scenarios. This article provides a mathematical formula to estimate probable efficacy against COVID-19 when administering two vaccines in a specific population. These vaccines, given in a series, could be of different technologies and brands. [ABSTRACT FROM AUTHOR]

Objective. To determine the haematological parameters according to the reproductive status of Peruvian Paso horses in the Province of Lambayeque. Materials and methods. The research was conducted on 60 clinically healthy adult horses (> 4 years), without previous drug treatment. Four groups of 15 horses were formed: gelding, entire male, empty mare and pregnant mare. First, a general clinical examination was performed to confirm their good health. Blood was drawn from the jugular vein of all the horses. The samples were processed by haematological analysis and the parameters of the red series (haemoglobin, haematocrit, red blood cells, mean corpuscular volume [MCV], mean corpuscular haemoglobin [MCH] and the mean corpuscular haemoglobin concentration [MCHC] were determined. Likewise, the white series (leukocytes, neutrophils segmented and stacked, basophils, monocytes, lymphocytes, eosinophils) and the thrombocytic series were processed and the unit range determined. Manual methods, mathematical formulas and the Drabkin method were used in the clinical pathology laboratory. The Kruskal Wallis Statistical test was applied and consequently the mean, standard deviation and ranges of variables were obtained. Results. No significant statistical differences were found in the white, red and thrombocytic series according to sex or reproductive status, except the number of basophils was higher in the entire males. Conclusions. The haematological parameters according to the reproductive status of the Peruvian Step horse are within the normal ranges (as per the literature pertaining to this area). However, the number of lymphocytes was much lower. [ABSTRACT FROM AUTHOR]

The objective of this work was to study and model the dehydration kinetics of nixtamalized corn kernels with different steeping time (ST) in cooking-alkaline water. These corn kernels with ST lose moisture (LM) continuously by differential "dM" by time differential "dt." Both are proportional to the amount of moisture M (t) existing in hydrated corn kernels at time "t" plus a constant "C" (determined with the application of boundary conditions). "K" is the proportionality constant. The proposed differential equation has the mathematical structure: dM / dt = - K [M (t) + C]. When solving this differential equation and replacing boundary conditions, the solution was: M (t) = (M0-ME) eKt - ME. In conclusion, this study presents a mathematical hypothesis for this formula that many authors have used in their publications without having a mathematical hypothesis. [ABSTRACT FROM AUTHOR]

Copyright of Revista del Museo de Antropología is the property of Museo de Antropologia - IDACOR and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Despite the complexity of the planning development process, translating to euros the decisions adopted may increase the transparency of this process. As jurisprudence highlights, not only complex mathematical formulae should be considered, but also it is important to show through numbers the fact that planning may be profitable. Unfortunately, plan’s economic documents are sometimes not taken into account, or even if they exist, they prove to be inadequate, which enhance the annulment of the plan by tribunals. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work analyses the level of cognitive challenge on probability tasks proposed by Chilean Primary Education programs. Such programs establish a reference to follow when deciding how to organize, sequence and develop the teaching and learning process, especially about contents which have been recently incorporated into the school curriculum. Results show a low level of cognitive challenge tasks predominance; which lessen the study of probability to the use algorithms and formulas. Thus, it is necessary to emphasize aspects which foster the development of an understanding of probability which allows students to use, interpret and communicate ideas and information to solve real problems where uncertainty is present. [ABSTRACT FROM AUTHOR]

After a deep review of the mathematical formulas used in studies of lexical availability, we have found some inconvenient in the range of value in the original proposal formules which make difficult to compare researches which have different size of samples. Mainly, we refer to the formula for calculating lexical availability by Juan Carlos Lopez Chavez Frias Strassburger (1987, 1991) which shows problems to measure the rate of availability when words are close to the lower limit (0), that means, they are "very little available". On the other hand, the formula proposed by Ávila Muñoz and Sánchez Sáez (2010), which measures the degree of compatibility of term, although a word reaches the maximum compatibility, its value never reach 1, theoric upper reference limit in this formula. In this work we analyze the above described cases, and we propose different formulas which, allow greater mathematical precision, and also, allow comparability between different studies using samples of different sizes and characteristics. [ABSTRACT FROM AUTHOR]

Copyright of Gaceta de la Real Sociedad Matematica Espanola is the property of Real Sociedad Matematica Espanola and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work is intended to analyze and eventually assess the meaning of some theories of proportion, often posed from false premises of objectivity and scientific certainty. We seek to make evident the symbolic character of an important part of these systems. In this framework we weigh the assessment of metaphorical or poetic aspects. To that end, clichés and abuses of the theories obsessed in the definition of mathematical formulas that too often try to roughly certify themselves in all kind of examples are questioned. From these keys some aspects of Le Corbusier's Modulor are interpreted. [ABSTRACT FROM AUTHOR]

Copyright of Lámpsakos is the property of Fundacion Universitaria Luis Amigo, Facultad de Ingenierias and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mathematical formulas are obtained to computerize the calculation of effective velocity and depth in the hydraulic analysis of sewers with circular cross section for drainage systems. Tables and graphics of traditional methodology are analyzed, which after some treatment, derive into equations proposed here. The formulas were obtained using mathematical methods of curve fitting and for their validation the results achieved with the usual methodology were compared to those computed by the proposed equations and found to be totally reliable. The equations are of great value when integrated into a computer program, allowing automatic design without handbook consulting to establish accurate values to the variables involved. [ABSTRACT FROM AUTHOR]

Readability refers to the ease of reading and understanding a text. The need to ensure the readability of Web pages is related to universal access to products and services in the information society, which aims to provide an Internet for all. This article describes a study conducted to assess the readability of textual contents of Web portals of 40 universities at the top positions in international university rankings to determine whether the best universities have readable web pages. Mathematical formulas that evaluate syntactic difficulty of text oriented to texts written in English or in Spanish were applied. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The authors present a reproducible and simple method to evaluate scars from a cosmetic point of view. The use of digital photographs processed by means of computer programs enables us to carry out colorimetric measurements on the scar and adjacent healthy skin. Results can be expressed with mathematical formulae that make it possible to quantify the chromatic differences between both surfaces. The results obtained in 20 patients with pathological scars divided into 2 therapeutic series for 9 months were compared with this system. Ten patients received treatment with silicone gel and another 10 received photoprotector treatment. Colorimetry revealed in the independent study that statistically significant differences found between healthy and scar skin before treatment were maintained in the group treated with the photoprotector gel while they did not appear after administration of the silicone gel. The relativised colorimetric study (Scar-score) showed a significant recession in both groups but this was greater in the group treated with silicone gel. Both the bivariant and multivariant analysis revealed a significantly higher therapeutic benefit in the group treated with silicone gel compared to the photoprotector treatment. [ABSTRACT FROM AUTHOR]

In order to capture the maximum energy from the wind, control systems operating always at an optimum power has been utilized. This control system, considered as a whole, must be able of respond with an adequate precision and speed in response to the randomness and variability of the wind. The relationship between the wind speed, the blade pitch and the generator speed in order to produce the maximum power and also be able to limit the output power for large wind speeds is a very complicated one and it is very difficult to find its mathematical function. In this paper, the authors, utilizing the MATLAB SIMULINK toolboxes, propose representing this functional relation by means of an Artificial Neural Network (ANN). The parameters and characteristics of an existing wind turbine generator are utilized and it is demonstrated that it is possible to use an ANN in the simulation and control of a variable speed, variable pitch wind turbine that capture the maximum power from the wind. [ABSTRACT FROM AUTHOR]

A learning technique for a better conceptual understanding in physics is presented. This technique uses quotients and units in an intended way, defining a quotient as the starting point for this method. A qualitative experience mentioned shows that this method enhances a good understanding of physics concepts, allowing the development of new concepts. [ABSTRACT FROM AUTHOR]

This paper is framed in a Ph. D. Thesis titled "The role of the teacher in didactic situations that pose ruptures between arithmetic practices and algebraic practices". The thesis project aims at producing knowledge about the role of the teacher in the emergence of new ideas in the context of didactic situations that involve aspects of algebraic practice and confront the student with ruptures in his arithmetical practices. In this paper we are interested in focusing in the analysis of a part of the classroom register. In this analysis we try to interpret the senses that are played around the idea of "formula" in the part of the class destined to the sharing of results, in which the teacher organizes a discussion about the resolutions to a problem. [ABSTRACT FROM AUTHOR]

In the classical theory for calculation of dynamic loads coefficients in elements subdued to impact loads, frequently two fundamental methods are used. In one of those methods is not considered the mass of the element impacted, giving rise to a method of relatively simple solution. Nevertheless, some authors hold that more exactness in the calculations is obtained when mass of the impacted body is taken in account, which introduces high level of difficulty in the calculations. In this case, correcting factors that permit to determining the coefficients of dynamic loads are given in manuals and books for some typical cases only. In the present paper, through a study case, the comparison of calculations made by both methods is exposed. As a result is obtained that, when increase the relative magnitude of the impacted body mass with regard to that of the body that impacts, the calculation errors, product of the non consideration of the mass of the first one, are increased. [ABSTRACT FROM AUTHOR]

In 1999 Nina Virchenko have considered the τ-generalization of Gauss hypergeometric function 2R1(a, b; c; τ; z) with a set of recurrence relations and differentiation formulas. In this paper is obtained some indefined integrals associated with the generalized hypergeometric function and some particular cases. [ABSTRACT FROM AUTHOR]

This paper proposes a new kind of non-linear hybrid model. In the proposed model, mean non-linearity is represented by using an adaptive neuro-fuzzy inference system (ANFIS) whereas variance is represented using a conditional self-regressive heteroscedastic component. The mathematical formula for this type of model is shown and a method to estimate it is proposed. In addition, a specification strategy is developed for the proposed model, based on a battery of statistical soft transaction regression (STR) tests and on verosimility radius testing. As a case study, the IBM stock closing price series dynamics were modeled, which is commonly used as a benchmark in the literature on time series. Results indicate that the model developed represents the dynamics of the studied series better than other models with similar characteristics. [ABSTRACT FROM AUTHOR]

Copyright of Estudios Demográficos y Urbanos is the property of El Colegio de Mexico AC and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Introduction: Friedewald's formula is a method used to estimate the cholesterol-LDL (C-LDL) is inaccurate if the concentration of the seric tryglicerides is top of 400 mg/dL. Material and methods: They were included 25 patients of the masculine sex with triglycerides major of 400 mg/dL additional carried out the determinations of: total cholesterol and of different densities. To obtain the value of the cholesterol of low and very low density I use Friedelwald's formula and formulates one alternates. Results: The values obtained of C-LDL by Friedewald's formula are in the interval from -15.6 to 189.6, the average of 85.11 and the median of 79 mg/dL, with the alternate formula the values were from 98 to 282, with an average of 174.16 and the median of 169 mg/dL, on having realized an analysis of linear simple regression of CLDL's values obtained by Friedewald's formula and for the alternate formula a value obtained of r = 0.54 the difference of C-LDL's values obtained P = 0.0007. Conclusions: The Inaccuracy of Friedewald's formula, does imperative to unify the criteria for the calculation of the C-LDL in the patients who have a concentration major of triglycerides 400 mg/dL if one does not counted on the resources for realizing the direct determination. [ABSTRACT FROM AUTHOR]

Copyright of Universitas Médica is the property of Pontificia Universidad Javeriana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper are suggested several possible interpretations to the analogy mentioned by Lévi-Strauss in order to understand totemism as a kind of mental activity, similar to that implicit in Boole's algebra. For such purpose, there is an outline of the boolean representation on Lévi-Strauss proposed general formula of kinship. Ultimately this leads the author to suggest that "savage thinking" is similar to mathematical thought when working with algorithms. [ABSTRACT FROM AUTHOR]

The article presents a demonstration of Dobinski's formula from the Royal Spanish Mathematical Society.