Search results for: Feynman formulas

Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Petar Sarajcev, Josip Vasilj, Damir Jakus

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This paper presents a novel statistical description of the counterpoise effective length due to lightning surges, where the (impulse) effective length had been obtained by means of regressive formulas applied to the transient simulation results. The effective length is described in terms of a statistical distribution function, from which median, mean, variance, and other parameters of interest could be readily obtained. The influence of lightning current amplitude, lightning front duration, and soil resistivity on the effective length has been accounted for, assuming statistical nature of these parameters. A method for determining the optimal counterpoise length, in terms of the statistical impulse effective length, is also presented. It is based on estimating the number of dangerous events associated with lightning strikes. Proposed statistical description and the associated method provide valuable information which could aid the design engineer in optimising physical lengths of counterpoises in different grounding arrangements and soil resistivity situations.

Keywords: counterpoise, grounding conductor, effective length, lightning, Monte Carlo method, statistical distribution

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Authors: Zhicheng Han

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This study examines the correlation between knowledge of formulaic language, working memory (WM), and phonological short-term memory (PSTM) in Chinese L2 learners of English. This study investigates if WM and PSTM correlate differently to the acquisition of formulaic language, which may be relevant for the discourse around the conceptualization of formulas. Connectionist approaches have lead scholars to argue that formulas are form-meaning connections stored whole, making PSTM significant in the acquisitional process as it pertains to the storage and retrieval of chunk information. Generativist scholars, on the other hand, argued for active participation of interlanguage grammar in the acquisition and use of formulaic language, where formulas are represented in the mind but retain the internal structure built around a lexical core. This would make WM, especially the processing component of WM an important cognitive factor since it plays a role in processing and holding information for further analysis and manipulation. The current study asked L1 Chinese learners of English enrolled in graduate programs in China to complete a preference raking task where they rank their preference for formulas, grammatical non-formulaic expressions, and ungrammatical phrases with and without the lexical core in academic contexts. Participants were asked to rank the options in order of the likeliness of them encountering these phrases in the test sentences within academic contexts. Participants’ syntactic proficiency is controlled with a cloze test and grammar test. Regression analysis found a significant relationship between the processing component of WM and preference of formulaic expressions in the preference ranking task while no significant correlation is found for PSTM or syntactic proficiency. The correlational analysis found that WM, PSTM, and the two proficiency test scores have significant covariates. However, WM and PSTM have different predictor values for participants’ preference for formulaic language. Both storage and processing components of WM are significantly correlated with the preference for formulaic expressions while PSTM is not. These findings are in favor of the role of interlanguage grammar and syntactic knowledge in the acquisition of formulaic expressions. The differing effects of WM and PSTM suggest that selective attention to and processing of the input beyond simple retention play a key role in successfully acquiring formulaic language. Similar correlational patterns were found for preferring the ungrammatical phrase with the lexical core of the formula over the ones without the lexical core, attesting to learners’ awareness of the lexical core around which formulas are constructed. These findings support the view that formulaic phrases retain internal syntactic structures that are recognized and processed by the learners.

Keywords: formulaic language, working memory, phonological short-term memory, academic language

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Authors: Gerardo Casal, Miguel E. Vázquez-Méndez

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The clothoid (also known as Cornu spiral or Euler spiral) is a curve that is characterized because its curvature is proportional to its length. This property makes that it would be widely used as transition curve for designing the layout of roads and railway tracks. In this work, from the geometrical property characterizing the clothoid, its parametric equations are obtained and two algorithms to compute it are compared. The first (classical), is widely used in Surveying Schools and it is based on the use of explicit formulas obtained from Taylor expansions of sine and cosine functions. The second one (alternative) is a very simple algorithm, based on the numerical solution of the initial value problems giving the clothoid parameterization. Both methods are compared in some typical surveying problems. The alternative method does not use complex formulas and so it is conceptually very simple and easy to apply. It gives good results, even if the classical method goes wrong (if the quotient between length and radius of curvature is high), needs no subsequent translations nor rotations and, consequently, it seems an efficient tool for designing the layout of roads and railway tracks.

Keywords: transition curves, railroad and highway engineering, Runge-Kutta methods

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Authors: Michel Soto Chalhoub

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Building code-related literature provides recommendations on normalizing approaches to the calculation of the dynamic properties of structures. Most building codes make a distinction among types of structural systems, construction material, and configuration through a numerical coefficient in the expression for the fundamental period. The period is then used in normalized response spectra to compute base shear. The typical parameter used in simplified code formulas for the fundamental period is overall building height raised to a power determined from analytical and experimental results. However, reinforced concrete buildings which constitute the majority of built space in less developed countries pose additional challenges to the ones built with homogeneous material such as steel, or with concrete under stricter quality control. In the present paper, the particularities of reinforced concrete buildings are explored and related to current methods of equivalent static analysis. A comparative study is presented between the Uniform Building Code, commonly used for buildings within and outside the USA, and data from the Middle East used to model 151 reinforced concrete buildings of varying number of bays, number of floors, overall building height, and individual story height. The fundamental period was calculated using eigenvalue matrix computation. The results were also used in a separate regression analysis where the computed period serves as dependent variable, while five building properties serve as independent variables. The statistical analysis shed light on important parameters that simplified code formulas need to account for including individual story height, overall building height, floor plan, number of bays, and concrete properties. Such inclusions are important for reinforced concrete buildings of special conditions due to the level of concrete damage, aging, or materials quality control during construction. Overall results of the present analysis show that simplified code formulas for fundamental period and base shear may be applied but they require revisions to account for multiple parameters. The conclusion above is confirmed by the analytical model where fundamental periods were computed using numerical techniques and eigenvalue solutions. This recommendation is particularly relevant to code upgrades in less developed countries where it is customary to adopt, and mildly adapt international codes. We also note the necessity of further research using empirical data from buildings in Lebanon that were subjected to severe damage due to impulse loading or accelerated aging. However, we excluded this study from the present paper and left it for future research as it has its own peculiarities and requires a different type of analysis.

Keywords: seismic behaviour, reinforced concrete, simplified code formulas, equivalent static analysis, base shear, response spectra

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Authors: Piotr Ciuman, Barbara Lipska

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The aim of presented research was to improve numerical predictions of air parameters distribution in the actual natatorium by the selection of calculation formula of mass flux of moisture emitted from the pool. Selected correlation should ensure the best compliance of numerical results with the measurements' results of these parameters in the facility. The numerical model of the natatorium was developed, for which boundary conditions were prepared on the basis of measurements' results carried out in the actual facility. Numerical calculations were carried out with the use of ANSYS CFX software, with six formulas being implemented, which in various ways made the moisture emission dependent on water surface temperature and air parameters in the natatorium. The results of calculations with the use of these formulas were compared for air parameters' distributions: Specific humidity, velocity and temperature in the facility. For the selection of the best formula, numerical results of these parameters in occupied zone were validated by comparison with the measurements' results carried out at selected points of this zone.

Keywords: experimental validation, indoor swimming pool, moisture emission, natatorium, numerical calculations CFD, thermal and humidity conditions, ventilation

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Authors: Said Benkaciali, Mourad Haddadi, Abdallah Khellaf, Kacem Gairaa, Mawloud Guermoui

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In this study, many experiments were carried out to assess the influence of the input parameters on the performance of multilayer perceptron which is one the configuration of the artificial neural networks. To estimate the daily global solar radiation on the horizontal surface, we have developed some models by using seven combinations of twelve meteorological and geographical input parameters collected from a radiometric station installed at Ghardaïa city (southern of Algeria). For selecting of best combination which provides a good accuracy, six statistical formulas (or statistical indicators) have been evaluated, such as the root mean square errors, mean absolute errors, correlation coefficient, and determination coefficient. We noted that multilayer perceptron techniques have the best performance, except when the sunshine duration parameter is not included in the input variables. The maximum of determination coefficient and correlation coefficient are equal to 98.20 and 99.11%. On the other hand, some empirical models were developed to compare their performances with those of multilayer perceptron neural networks. Results obtained show that the neural networks techniques give the best performance compared to the empirical models.

Keywords: empirical models, multilayer perceptron neural network, solar radiation, statistical formulas

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Authors: Mustafa M. Donma, Orkide Donma

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The number of indices developed for the evaluation of obesity both in adults and pediatric population is ever increasing. These indices are also used in cases with metabolic syndrome (MetS), mostly the ultimate form of morbid obesity. Aside from anthropometric measurements, formulas constituted using these parameters also find clinical use. These formulas can be listed as two groups; being weight-dependent and –independent. Some are extremely sophisticated equations and their clinical utility is questionable in routine clinical practice. The aim of this study is to compare presently available obesity indices and find the most practical one. Their associations with MetS components were also investigated to determine their capacities in differential diagnosis of morbid obesity with and without MetS. Children with normal body mass index (N-BMI) and morbid obesity were recruited for this study. Three groups were constituted. Age- and sex- dependent BMI percentiles for morbid obese (MO) children were above 99 according to World Health Organization tables. Of them, those with MetS findings were evaluated as MetS group. Children, whose values were between 85 and 15 were included in N-BMI group. The study protocol was approved by the Ethics Committee of the Institution. Parents filled out informed consent forms to participate in the study. Anthropometric measurements and blood pressure values were recorded. Body mass index, hip index (HI), conicity index (CI), triponderal mass index (TPMI), body adiposity index (BAI), body shape index (ABSI), body roundness index (BRI), abdominal volume index (AVI), waist-to-hip ratio (WHR) and waist circumference+hip circumference/2 ((WC+HC)/2) were the formulas examined within the scope of this study. Routine biochemical tests including fasting blood glucose (FBG), insulin (INS), triglycerides (TRG), high density lipoprotein-cholesterol (HDL-C) were performed. Statistical package program SPSS was used for the evaluation of study data. p<0.05 was accepted as the statistical significance degree. Hip index did not differ among the groups. A statistically significant difference was noted between N-BMI and MetS groups in terms of ABSI. All the other indices were capable of making discrimination between N-BMI-MO, N-BMI- MetS and MO-MetS groups. No correlation was found between FBG and any obesity indices in any groups. The same was true for INS in N-BMI group. Insulin was correlated with BAI, TPMI, CI, BRI, AVI and (WC+HC)/2 in MO group without MetS findings. In MetS group, the only index, which was correlated with INS was (WC+HC)/2. These findings have pointed out that complicated formulas may not be required for the evaluation of the alterations among N-BMI and various obesity groups including MetS. The simple easily computable weight-independent index, (WC+HC)/2, was unique, because it was the only index, which exhibits a valuable association with INS in MetS group. It did not exhibit any correlation with other obesity indices showing associations with INS in MO group. It was concluded that (WC+HC)/2 was pretty valuable practicable index for the discrimination of MO children with and without MetS findings.

Keywords: children, insulin, metabolic syndrome, obesity indices

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Authors: Samuel J. Ahmad, Michael Zhu, Andrew J. Kobets

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Segmentation tools continue to advance, evolving from manual methods to automated contouring technologies utilizing convolutional neural networks. These techniques have evaluated ventricular and hemorrhagic volumes in the past but may be applied in novel ways to assess posterior fossa-associated pathologies such as Chiari malformations. Herein, we summarize literature pertaining to segmentation in the context of this and other posterior fossa-based diseases such as trigeminal neuralgia, hemifacial spasm, and posterior fossa syndrome. A literature search for volumetric analysis of the posterior fossa identified 27 papers where semi-automated, automated, manual segmentation, linear measurement-based formulas, and the Cavalieri estimator were utilized. These studies produced superior data than older methods utilizing formulas for rough volumetric estimations. The most commonly used segmentation technique was semi-automated segmentation (12 studies). Manual segmentation was the second most common technique (7 studies). Automated segmentation techniques (4 studies) and the Cavalieri estimator (3 studies), a point-counting method that uses a grid of points to estimate the volume of a region, were the next most commonly used techniques. The least commonly utilized segmentation technique was linear measurement-based formulas (1 study). Semi-automated segmentation produced accurate, reproducible results. However, it is apparent that there does not exist a single semi-automated software, open source or otherwise, that has been widely applied to the posterior fossa. Fully-automated segmentation via such open source software as FSL and Freesurfer produced highly accurate posterior fossa segmentations. Various forms of segmentation have been used to assess posterior fossa pathologies and each has its advantages and disadvantages. According to our results, semi-automated segmentation is the predominant method. However, atlas-based automated segmentation is an extremely promising method that produces accurate results. Future evolution of segmentation technologies will undoubtedly yield superior results, which may be applied to posterior fossa related pathologies. Medical professionals will save time and effort analyzing large sets of data due to these advances.

Keywords: chiari, posterior fossa, segmentation, volumetric

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Authors: Hicham Gourgue, Ahmed Aharoune, Ahmed Ihlal

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We present in this work our model of road traffic emissions (line sources) and dispersion of these emissions, named DISPOLSPEM (Dispersion of Poly Sources and Pollutants Emission Model). In its emission part, this model was designed to keep the consistent bottom-up and top-down approaches. It also allows to generate emission inventories from reduced input parameters being adapted to existing conditions in Morocco and in the other developing countries. While several simplifications are made, all the performance of the model results are kept. A further important advantage of the model is that it allows the uncertainty calculation and emission rate uncertainty according to each of the input parameters. In the dispersion part of the model, an improved line source model has been developed, implemented and tested against a reference solution. It provides improvement in accuracy over previous formulas of line source Gaussian plume model, without being too demanding in terms of computational resources. In the case study presented here, the biggest errors were associated with the ends of line source sections; these errors will be canceled by adjacent sections of line sources during the simulation of a road network. In cases where the wind is parallel to the source line, the use of the combination discretized source and analytical line source formulas minimizes remarkably the error. Because this combination is applied only for a small number of wind directions, it should not excessively increase the calculation time.

Keywords: air pollution, dispersion, emissions, line sources, road traffic, urban transport

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Authors: B. Manikandan, A. Vijayaprabhu

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The conservative reversible gates are used to designed reversible sequential circuits. The sequential circuits are flip-flops and latches. The conservative logic gates are Feynman, Toffoli, and Fredkin. The design of two vectors testable sequential circuits based on conservative logic gates. All sequential circuit based on conservative logic gates can be tested for classical unidirectional stuck-at faults using only two test vectors. The two test vectors are all 1s, and all 0s. The designs of two vectors testable latches, master-slave flip-flops and double edge triggered (DET) flip-flops are presented. We also showed the application of the proposed approach toward 100% fault coverage for single missing/additional cell defect in the quantum- dot cellular automata (QCA) layout of the Fredkin gate. The conservative logic gates are in terms of complexity, speed, and area.

Keywords: DET, QCA, reversible logic gates, POS, SOP, latches, flip flops

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Authors: Soumia Merat, Lynda Djerbal, Ramdane Bahar, Mohammed Amin Benbouras

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Along with shear wave, many soil parameters are associated with the standard penetration test (SPT) as a dynamic in situ experiment. Both SPT-N data and geophysical data do not often exist in the same area. Statistical analysis of correlation between these parameters is an alternate method to estimate Vₛ conveniently and without additional investigations or data acquisition. Shear wave velocity is a basic engineering tool required to define dynamic properties of soils. In many instances, engineers opt for empirical correlations between shear wave velocity (Vₛ) and reliable static field test data like standard penetration test (SPT) N value, CPT (Cone Penetration Test) values, etc., to estimate shear wave velocity or dynamic soil parameters. The relation between Vs and SPT- N values of Algiers area is predicted using the collected data, and it is also compared with the previously suggested formulas of Vₛ determination by measuring Root Mean Square Error (RMSE) of each model. Algiers area is situated in high seismic zone (Zone III [RPA 2003: réglement parasismique algerien]), therefore the study is important for this region. The principal aim of this paper is to compare the field measurements of Down-hole test and the empirical models to show which one of these proposed formulas are applicable to predict and deduce shear wave velocity values.

Keywords: empirical models, RMSE, shear wave velocity, standard penetration test

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Authors: Maarten J. Van der Burgt

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A universe containing matter and antimatter can only exist when matter and antimatter repel each other. Such a system, where like attracts like and like repels unlike, will always expand. Calculations made for such a symmetric universe demonstrate that the expansion is consistent with Hubble’s law, the observed increase in the expansion velocity with time, the initial high acceleration and the foam structure of the universe. Conversely, these observations can be considered as proof for a symmetrical universe and for antimatter possessing a negative gravitational mass. A second proof can be found by reinterpreting the behavior of relativistic moving charged particles. Attributing their behavior to a charge defect of √(1-v2/c2) instead of to a mass defect of 1/√(1-v2/c2) makes it plausible that gravitation is an electromagnetic force, as already suggested by Feynman. This would automatically imply that antimatter has a negative gravitational mass. These proofs underpin the untenability of the Weak Equivalence Principle which states that in a gravitational field all structure less point-like particles follow the same path.

Keywords: celestial mechanics, cosmology, gravitation astrophysics, origin of structure, miscellaneous (matter and antimatter)

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Authors: Banafsheh Aghamohammadi, Masoud Honarvar, Babak Ghiassi Tarzi

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Usage of different components has been considered to improve the quality and nutritional properties of cakes in recent years. The effects of applying some sweeteners, instead of sugar, have been evaluated in cakes and many bread formulas up to now; but there has not been any research about the usage of by-products of sugar factories such as Wash and Green-A Syrups in cake formulas. In this research, the effects of substituting 25%, 50%, 75% and 100% of sugar with Wash and Green-A Syrups on some dough and cake properties, such as pH, viscosity, density, volume, weight loss, moisture, water activity, texture, staling, color and sensory evaluations, are studied. The results of these experiments showed that the pH values were not significantly different among any of the all cake batters and also most of the cake samples. Although differences among viscosity and specific gravity of all treatments were both significant and insignificant, these two parameters resulted in higher volume in all samples than the blank one. The differences in weight loss, moisture content and water activity of samples were insignificant. Evaluating of texture showed that the softness of most of samples is increased and the staling is decreased. Crumb color and sensory evaluations of samples were also affected by the replacement of sucrose with Wash and Green-A Syrups. According to the results, we can increase the shelf life and improve the quality and nutritional values of cake by using these kinds of syrups in the formulation.

Keywords: cake, green-A syrup, quality tests, sensory evaluation, wash syrup

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Authors: Seyed M. Khatami, H. Naderpour, R. Vahdani, R. C. Barros

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Many previous studies have been carried out to calculate the impact force and the dissipated energy between two neighboring buildings during seismic excitation, when they collide with each other. Numerical studies are an important part of impact, which several researchers have tried to simulate the impact by using different formulas. Estimation of the impact force and the dissipated energy depends significantly on some parameters of impact. Mass of bodies, stiffness of spring, coefficient of restitution, damping ratio of dashpot and impact velocity are some known and unknown parameters to simulate the impact and measure dissipated energy during collision. Collision is usually shown by force-displacement hysteresis curve. The enclosed area of the hysteresis loop explains the dissipated energy during impact. In this paper, the effect of using different types of impact models is investigated in order to calculate the impact force. To increase the accuracy of impact model and to optimize the results of simulations, a new damping equation is assumed and is validated to get the best results of impact force and dissipated energy, which can show the accuracy of suggested equation of motion in comparison with other formulas. This relation is called "n-m". Based on mathematical relation, an initial value is selected for the mentioned coefficients and kinetic energy loss is calculated. After each simulation, kinetic energy loss and energy dissipation are compared with each other. If they are equal, selected parameters are true and, if not, the constant of parameters are modified and a new analysis is performed. Finally, two unknown parameters are suggested to estimate the impact force and calculate the dissipated energy.

Keywords: impact force, dissipated energy, kinetic energy loss, damping relation

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Authors: Emmanuelle Merat, Arnaud Aubert, Sophie Cambos, Francis Vial, Patrick Beau

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Basically, consumers are sensitive to many stimuli when applying a cream: brand, packaging and indeed formulation compositions. Many studies demonstrated the influence of some stimuli such as brand, packaging, formula color and odor (e.g. in make-up applications). Those parameters influence perceived quality of the product. The objective of this work is to further investigate the relationship between nude skincare basic compositions with different textures and consumer experience. A tentative final step will be to connect the consumer feelings with key ingredients in the compositions. A new approach was developed to better understand touch-related subjective experience in consumers based on a combination of methods: sensory analysis with ten experts, preference mapping on one hundred female consumers and emotional assessments on thirty consumers (verbal and non-verbal through prosody and gesture monitoring). Finally, a methodology based on ‘sensorial trip’ (after olfactory, haptic and musical stimuli) has been experimented on the most interesting textures with 10 consumers. The results showed more or less impact depending on compositions and also on key ingredients. Three types of formulation particularly attracted the consumer: an aqueous gel, an oil-in-water emulsion, and a patented gel-in-oil formulation type. Regarding these three formulas, the preferences were both revealed through sensory and emotion tests. One was recognized as the most innovative in consumer sensory test whereas the two other formulas were discriminated in emotions evaluation. The positive emotions were highlighted especially in prosody criteria. The non-verbal analysis, which corresponds to the physical parameters of the voice, showed high pitch and amplitude values; linked to positive emotions. Verbatim, verbal content of responses (i.e., ideas, concepts, mental images), confirmed the first conclusion. On the formulas selected for their positive emotions generation, the ‘sensorial trip’ provided complementary information to characterize each emotional profile. In the second step, dedicated to better understand ingredients power, two types of ingredients demonstrated an obvious input on consumer preference: rheology modifiers and emollients. As a conclusion, nude cosmetic compositions with well-chosen textures and ingredients can positively stimulate consumer emotions contributing to capture their preference. For a complete achievement of the study, a global approach (Asia, America territories...) should be developed.

Keywords: sensory, emotion, cosmetic formulations, ingredients' influence

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: Seyyd Hossein Jafari-Petroudi, Maryam Pirouz

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This note is devoted to (k; h)-Jacobsthal sequence as a general term of particular series. More formulas for nth term and sum of the first n terms of series that their general terms are (k; h)-Jacobsthal sequence and (k; h)-Jacobsthal-Petroudi sequence are derived. Finally other properties of these sequences are represented.

Keywords: (k, h)-Jacobsthal sequence, (k, h)-Jacobsthal Petroudisequence, recursive relation, sum

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Authors: Fadi Awawdeh

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In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: identification problems, semigroup theory, methods for inverse problems, scientific computing

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Authors: Deniz Ünal Özpalamutcu, Burcu Altman

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Actuaria uses mathematics, statistic and financial information when analyzing the financial impacts of uncertainties, risks, insurance and pension related issues. In other words, it deals with the likelihood of potential risks, their financial impacts and especially the financial measures. Handling these measures require some long-term payment and investments. So, it is obvious it is inevitable to plan the periodic payments with equal time intervals considering also the changing value of money over time. These series of payment made specific intervals of time is called annuity or rant. In literature, rants are classified based on start and end dates, start times, payments times, payments amount or frequency. Classification of rants based on payment amounts changes based on the constant, descending or ascending payment methods. The literature about handling the annuity is very limited. Yet in a daily life, especially in today’s world where the economic issues gained a prominence, it is very crucial to use the variable annuity method in line with the demands of the customers. In this study, the types of annuities with flexible payment are discussed. In other words, we focus on calculating payment amount of a period by adding a certain percentage of previous period payment was studied. While studying this problem, formulas were created considering both start and end period payments for cash value and accumulated. Also increase of each period payment by r interest rate each period payments calculated with previous periods increases. And the problem of annuities (rants) of which each period payment increased with previous periods’ increase by r interest rate has been analyzed. Cash value and accumulated value calculation of this problem were studied separately based on the period start/end and their relations were expressed by formulas.

Keywords: actuaria, annuity, flexible payment, rant

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Authors: Katarzyna Baruch, Agata Szelag, Aleksandra Majchrzak, Tadeusz Kamisinski

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Methodology of measurement of sound absorption coefficient in scaled models is based on the ISO 354 standard. The measurement is realised indirectly - the coefficient is calculated from the reverberation time of an empty chamber as well as a chamber with an inserted sample. It is crucial to maintain the atmospheric conditions stable during both measurements. Possible differences may be amended basing on the formulas for atmospheric attenuation coefficient α given in ISO 9613-1. Model studies require scaling particular factors in compliance with specified characteristic numbers. For absorption coefficient measurement, these are for example: frequency range or the value of attenuation coefficient m. Thanks to the possibilities of modern electroacoustic transducers, it is no longer a problem to scale the frequencies which have to be proportionally higher. However, it may be problematic to reduce values of the attenuation coefficient. It is practically obtained by drying the air down to a defined relative humidity. Despite the change of frequency range and relative humidity of the air, ISO 9613-1 standard still allows the calculation of the amendment for little differences of the atmospheric conditions in the chamber during measurements. The paper discusses a number of theoretical analyses and experimental measurements performed in order to obtain consistency between the values of attenuation coefficient calculated from the formulas given in the standard and by measurement. The authors performed measurements of reverberation time in a chamber made in a 1/8 scale in a corresponding frequency range, i.e. 800 Hz - 40 kHz and in different values of the relative air humidity (40% 5%). Based on the measurements, empirical values of attenuation coefficient were calculated and compared with theoretical ones. In general, the values correspond with each other, but for high frequencies and low values of relative air humidity the differences are significant. Those discrepancies may directly influence the values of measured sound absorption coefficient and cause errors. Therefore, the authors made an effort to determine an amendment minimizing described inaccuracy.

Keywords: air absorption correction, attenuation coefficient, dimensional analysis, model study, scaled modelling

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Authors: Parul Jindal, Shubhi Singh, Priya Ramakrishnan, Shailender Raghuvanshi

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Background: Knowledge of the influence of the age of the child on laryngeal dimensions is essential for all practitioners who are dealing with paediatric airway. Choosing the correct endotracheal tube (ETT) size is a crucial step in pediatric patients because a large-sized tube may cause complications like post-extubation stridor and subglottic stenosis. On the other hand with a smaller tube, there will be increased gas flow resistance, aspiration risk, poor ventilation, inaccurate monitoring of end-tidal gases and reintubation may also be required with a different size of the tracheal tube. Recent advancement in ultrasonography (USG) techniques should now allow for accurate and descriptive evaluation of pediatric airway. Aims and objectives: This study was planned to determine the accuracy of Ultrasonography (USG) to assess the appropriate ETT size and compare it with physical indices based formulae. Methods: After obtaining approval from Institute’s Ethical and Research committee, and parental written and informed consent, the study was conducted on 100 subjects of either sex between 12-60 months of age, undergoing various elective surgeries under general anesthesia requiring endotracheal intubation. The same experienced radiologist performed ultrasonography. The transverse diameter was measured at the level of cricoids cartilage by USG. After USG, general anesthesia was administered using standard techniques followed by the institute. An experienced anesthesiologist performed the endotracheal intubations with uncuffed endotracheal tube (Portex Tracheal Tube Smiths Medical India Pvt. Ltd.) with Murphy’s eye. He was unaware of the finding of the ultrasonography. The tracheal tube was considered best fit if air leak was satisfactory at 15-20 cm H₂O of airway pressure. The obtained values were compared with the values of endotracheal tube size calculated by ultrasonography, various age, height, weight-based formulas and diameter of right and left little finger. The correlation of the size of the endotracheal tube by different modalities was done and Pearson's correlation coefficient was obtained. The comparison of the mean size of the endotracheal tube by ultrasonography and by traditional formula was done by the Friedman’s test and Wilcoxon sign-rank test. Results: The predicted tube size was equal to best fit and best determined by ultrasonography (100%) followed by comparison to left little finger (98%) and right little finger (97%) and age-based formula (95%) followed by multivariate formula (83%) and body length (81%) formula. According to Pearson`s correlation, there was a moderate correlation of best fit endotracheal tube with endotracheal tube size by age-based formula (r=0.743), body length based formula (r=0.683), right little finger based formula (r=0.587), left little finger based formula (r=0.587) and multivariate formula (r=0.741). There was a strong correlation with ultrasonography (r=0.943). Ultrasonography was the most sensitive (100%) method of prediction followed by comparison to left (98%) and right (97%) little finger and age-based formula (95%), the multivariate formula had an even lesser sensitivity (83%) whereas body length based formula was least sensitive with a sensitivity of 78%. Conclusion: USG is a reliable method of estimation of subglottic diameter and for prediction of ETT size in children.

Keywords: endotracheal intubation, pediatric airway, subglottic diameter, traditional formulas, ultrasonography

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: Bozena Dohnalkova

Abstract:

This paper presents a part of the project solving which is dedicated to the identification of the hazardous waste with the most critical production within the Czech Republic with the aim to study and find the optimal composition of the cement matrix that will ensure maximum content disposal of chosen hazardous waste. In the first stage of project solving – which represents this paper – a specific hazardous waste was chosen, its properties were identified and suitable solidification agents were chosen. Consequently solidification formulas and testing methodology was proposed.

Keywords: cementation, solidification, waste, binder

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Authors: Lina Wu, Jia Liu, Ye Li

Abstract:

The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner formula, Calculus Stokes' Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Liouville-type problem, p-harmonic map

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

Abstract:

Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

Procedia PDF Downloads 425

Authors: Quan Wen, Tianxiao Chang, Shaolu Shi, Yushi Wang, Guangyu Wang

Abstract:

As a kind of working environment of the fuze, the spin rate decaying law of projectile in exterior trajectory is of great value in the design of the rotation count fixed distance fuze. In addition, it is significant in the field of devices for simulation tests of fuze exterior ballistic environment, flight stability, and dispersion accuracy of gun projectile and opening and scattering design of submunition and illuminating cartridges. Besides, the self-destroying mechanism of the fuze in small-caliber projectile often works by utilizing the attenuation of centrifugal force. In the theory of projectile aerodynamics and fuze design, there are many formulas describing the change law of projectile angular velocity in external ballistic such as Roggla formula, exponential function formula, and power function formula. However, these formulas are mostly semi-empirical due to the poor test conditions and insufficient test data at that time. These formulas are difficult to meet the design requirements of modern fuze because they are not accurate enough and have a narrow range of applications now. In order to provide more accurate ballistic environment parameters for the design of a hemispherical head projectile fuze, the projectile’s spin rate decaying law in exterior trajectory under the effect of air resistance was studied. In the analysis, the projectile shape was simplified as hemisphere head, cylindrical part, rotating band part, and anti-truncated conical tail. The main assumptions are as follows: a) The shape and mass are symmetrical about the longitudinal axis, b) There is a smooth transition between the ball hea, c) The air flow on the outer surface is set as a flat plate flow with the same area as the expanded outer surface of the projectile, and the boundary layer is turbulent, d) The polar damping moment attributed to the wrench hole and rifling mark on the projectile is not considered, e) The groove of the rifle on the rotating band is uniform, smooth and regular. The impacts of the four parts on aerodynamic moment of the projectile rotation were obtained by aerodynamic theory. The surface friction stress of the projectile, the polar damping moment formed by the head of the projectile, the surface friction moment formed by the cylindrical part, the rotating band, and the anti-truncated conical tail were obtained by mathematical derivation. After that, the mathematical model of angular spin rate attenuation was established. In the whole trajectory with the maximum range angle (38°), the absolute error of the polar damping torque coefficient obtained by simulation and the coefficient calculated by the mathematical model established in this paper is not more than 7%. Therefore, the credibility of the mathematical model was verified. The mathematical model can be described as a first-order nonlinear differential equation, which has no analytical solution. The solution can be only gained as a numerical solution by connecting the model with projectile mass motion equations in exterior ballistics.

Keywords: ammunition engineering, fuze technology, spin rate, numerical simulation

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Authors: Bojan Radisic, Katarina Stavlic

Abstract:

The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples.

Keywords: consumer surplus, producer surplus, definite integral, integration

Procedia PDF Downloads 550

Authors: Soner Nandappa D., Ahmed Mohammed Naji

Abstract:

In a graph G = (V, E), the distance from a vertex v to a vertex u is the length of shortest v to u path. The eccentricity e(v) of v is the distance to a farthest vertex from v. The diameter diam(G) is the maximum eccentricity. The k-distance neighborhood of v, for 0 ≤ k ≤ e(v), is Nk(v) = {u ϵ V (G) : d(v, u) = k}. In this paper, we introduce a new distance degree based topological polynomial of a graph G is called a k- distance neighborhood polynomial, denoted Nk(G, x). It is a polynomial with the coefficient of the term k, for 0 ≤ k ≤ e(v), is the sum of the cardinalities of Nk(v) for every v ϵ V (G). Some properties of k- distance neighborhood polynomials are obtained. Exact formulas of the k- distance neighborhood polynomial for some well-known graphs, Cartesian product and join of graphs are presented.

Keywords: vertex degrees, distance in graphs, graph operation, Nk-polynomials

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Authors: Frantisek Mosna

Abstract:

E-learning has become an efficient and widespread means in process of education at all branches of human activities. Statistics is not an exception. Unfortunately the main focus in the statistics teaching is usually paid to the substitution to formulas. Suitable web-sites can simplify and automate calculation and provide more attention and time to the basic principles of statistics, mathematization of real-life situations and following interpretation of results. We introduce our own web-sites for hypothesis testing. Their didactic aspects, technical possibilities of individual tools for their creating, experience and advantages or disadvantages of them are discussed in this paper. These web-sites do not substitute common statistical software but significantly improve the teaching of the statistics at universities.

Keywords: e-learning, hypothesis testing, PHP, web-sites

Procedia PDF Downloads 398