Статті в журналах: "Paradifferential calculus with parameters"

1

Hua, Chen, and Luigi Rodino. "Paradifferential calculus in Gevrey classes." Journal of Mathematics of Kyoto University 41, no. 1 (2001): 1–31. http://dx.doi.org/10.1215/kjm/1250517647.

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2

Xiang, Zhaoyin, and Wei Yan. "On the Well-Posedness of the Boussinesq Equation in the Triebel-Lizorkin-Lorentz Spaces." Abstract and Applied Analysis 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/573087.

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We establish the local well-posedness and obtain a blow-up criterion of smooth solutions for the Boussinesq equations in the framework of Triebel-Lizorkin-Lorentz spaces. The main ingredients of our proofs are Littlewood-Paley decomposition and the paradifferential calculus.

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3

Sango, Mamadou, and Tesfalem Abate Tegegn. "Harmonic analysis tools for stochastic magnetohydrodynamics equations in Besov spaces." International Journal of Modern Physics B 30, no. 28n29 (November 10, 2016): 1640025. http://dx.doi.org/10.1142/s0217979216400257.

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We establish a regularity result for stochastic heat equations in probabilistic evolution spaces of Besov type and we use it to prove a global in time existence and uniqueness of solution to a stochastic magnetohydrodynamics equation. The existence result holds with a positive probability which can be made arbitrarily close to one. The work is carried out by blending harmonic analysis tools such as Littlewood–Paley decomposition, Jean–Micheal Bony paradifferential calculus and stochastic calculus. The law of large numbers is a key tool in our investigation. Our global existence result is new in three-dimensional spaces.

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4

Fons-Badal, Carla, Antonio Fons-Font, Carlos Labaig-Rueda, M. Fernanda Solá-Ruiz, Eduardo Selva-Otaolaurruchi, and Rubén Agustín-Panadero. "Analysis of Predisposing Factors for Rapid Dental Calculus Formation." Journal of Clinical Medicine 9, no. 3 (March 20, 2020): 858. http://dx.doi.org/10.3390/jcm9030858.

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Background: Calculus accumulation varies widely between individuals. Dental calculus has been associated with the principal periodontal diseases. The aim of this study was to analyze individual characteristics, and salivary and microbiological parameters among patients considered to be rapid calculus formers and patients who form calculus slowly. Methods: Individual characteristics were recorded in a sample of 74 patients (age, sex, smoking, periodontal diagnosis, and dental crowding), as well as salivary parameters (unstimulated saliva flow, pH, and biochemical analysis of saliva) and microbiological parameters (by means of semi-quantitative polymerase chain reaction (PCR) analysis). Results: A statistically significant association (p = 0.002) was found between the rate of calculus formation and the diagnosis of periodontal disease. A greater presence of dental crowding was observed among the group of rapid calculus formers. Urea and phosphorus levels were higher among rapid calculus formers. Regarding microbiological parameters, differences were found in Streptococcus mutans, this being higher in the group of slow formers. Conclusions: Rapid calculus formation appears to be linked to patients diagnosed with more severe periodontal diseases. Rapid calculus-forming patients present more dental crowding and a lower proportion of S. mutans.

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5

Corless, Robert M., David J. Jeffrey, and David R. Stoutemyer. "Integrals of functions containing parameters." Mathematical Gazette 104, no. 561 (October 8, 2020): 412–26. http://dx.doi.org/10.1017/mag.2020.96.

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Calculus students are taught that an indefinite integral is defined only up to an additive constant, and as a consequence generations of students have assiduously added ‘+C’ to their calculus homework. Although ubiquitous, these constants rarely garner much attention, and typically loiter without intent around the ends of equations, feeling neglected. There is, however, useful work they can do, work which is particularly relevant in the contexts of integral tables and computer algebra systems. We begin, therefore, with a discussion of the context, before returning to coax the constants out of the shadows and assign them their tasks.

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6

Năstăsescu, Vasile, and Gheorghe Bârsan. "SPH method in numerical calculus of detonation parameters." Journal of Engineering Sciences and Innovation 4, no. 1 (March 5, 2019): 1–16. http://dx.doi.org/10.56958/jesi.2019.4.1.1.

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This paper presents some of our results in using of the Smoothed Particles Hydrodynamics (SPH) method for the numerical modelling of the detonation phenomena. The study of the detonation is very important for evaluation of different explosives and even for their design. The paper also presents, in a synthetically way, some fundamentals of the detonation. The numerical modelling of the detonation can be made by Finite Element Method (FEM), but using of the SPH method brings some important advantages because the large deformations, large distortions occur. If the FEM can be used in Arbitrary Lagrangian-Eulerian (ALE) formulation, the SPH method can easily works and next to it, some specific parameters (density variation, specific energy etc.) can be obtained and analyzed by post-processing. The numerical results (by FEM and by SPH method) are compared with theoretical results. The numerical study allowed us to analyse the influence of some explosive characteristics and of the circumstances (non confined and confined explosive) upon detonation parameters.

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7

Hackbusch, Wolfgang. "Numerical tensor calculus." Acta Numerica 23 (May 2014): 651–742. http://dx.doi.org/10.1017/s0962492914000087.

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The usual large-scale discretizations are applied to two or three spatial dimensions. The standard methods fail for higher dimensions because the data size increases exponentially with the dimension. In the case of a regular grid withngrid points per direction, a spatial dimensiondyieldsndgrid points. A grid function defined on such a grid is an example of a tensor of orderd. Here, suitable tensor formats help, since they try to approximate these huge objects by a much smaller number of parameters, which increases only linearly ind. In this way, data of sizend= 10001000can also be treated.This paper introduces the algebraic and analytical aspects of tensor spaces. The main part concerns the numerical representation of tensors and the numerical performance of tensor operations.

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8

Sarkar, Jyotirmoy, and Mamunur Rashid. "Estimating the Parameters of a Simple Linear Regression Model Without Using Differential Calculus." Journal of Probability and Statistical Science 20, no. 1 (October 3, 2022): 191–203. http://dx.doi.org/10.37119/jpss2022.v20i1.645.

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To estimate the parameters of a simple linear regression model, students who already know calculus can minimize the total squared deviations by setting its first-order partial derivatives to zero and solving simultaneously. For students who do not know calculus, most teachers/textbooks simply state the formulas without justifying them. Students accept the formulas on faith; and for given data, they evaluate the estimates using a calculator or a statistical software. In this paper, we justify the formulas without invoking calculus. We hope the users of statistics will benefit from our proposed justifications.

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9

Pena, Andra Elena, Florea Dorel Anania, and Miron Zapciu. "Research Regarding Software Developing for Machining Parameters Optimization Calculus." Applied Mechanics and Materials 656 (October 2014): 192–99. http://dx.doi.org/10.4028/www.scientific.net/amm.656.192.

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Establish of efficient machining parameters has been a problem that has confronted manufacturing industries for nearly a century, and is still the subject of many studies. Optimum machining parameters are of great concern in manufacturing environments, where economy of machining operation plays a key role in competitiveness in the market. The aim of this paper is to present a method to integrate advanced technology issues into a simple and intuitive application for machining parameters calculus. The goal is the development of a program easy to use in industry for CAM engineers and machine operators, that optimize the cutting parameters (in ways that diminish the defects – vibrations, cutting tool wear, machine tools wear – and reduce the power consumption) depending on a number of parameters determined by experimental and analytical calculation. The program will integrate calculus algorithms based on experimental data and analytical results with a simple and friendly user interface.

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10

AWAI, I., Y. ZHANG, T. ISHIDA, and T. SUZUKI. "Principles of Time Domain Calculus of Microwave Resonator Parameters." IEICE Transactions on Electronics E90-C, no. 12 (December 1, 2007): 2198–204. http://dx.doi.org/10.1093/ietele/e90-c.12.2198.

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11

NICOLIN, Bogdan Adrian, and Ilie NICOLIN. "Calculation of steering system parameters of a military training aircraft." INCAS BULLETIN 14, no. 4 (December 2, 2022): 213–24. http://dx.doi.org/10.13111/2066-8201.2022.14.4.18.

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The mechanical-hydraulic steering system of a military training aircraft is a technical problem for specialized engineers and it must be investigated and solved in a scientific manner using theoretical knowledge, calculus programs such as Mathcad, and CAD applications for design such as CATIA V5 which allows the preservation of practical experience and favors its dissemination for future similar calculation. The scope of this calculus is to demonstrate that the active moment developed by the two hydraulic cylinders is always bigger than the resisting moment opposing the steering action of the nose landing gear wheel generated by the frictional forces between the wheel and the running way.

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12

Hayes, Ian J. "Procedures and parameters in the real-time program refinement calculus." Science of Computer Programming 64, no. 3 (February 2007): 286–311. http://dx.doi.org/10.1016/j.scico.2006.06.002.

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13

Tudor, Ciprian A., and Frederi G. Viens. "Variations and estimators for self-similarity parameters via Malliavin calculus." Annals of Probability 37, no. 6 (November 2009): 2093–134. http://dx.doi.org/10.1214/09-aop459.

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14

Agrawal, Om P., Sami I. Muslih, and Dumitru Baleanu. "Generalized variational calculus in terms of multi-parameters fractional derivatives." Communications in Nonlinear Science and Numerical Simulation 16, no. 12 (December 2011): 4756–67. http://dx.doi.org/10.1016/j.cnsns.2011.05.002.

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15

IRAC-ASTAUD, MICHÈLE. "DIFFERENTIAL CALCULUS ON A THREE-PARAMETER OSCILLATOR ALGEBRA." Reviews in Mathematical Physics 08, no. 08 (November 1996): 1083–90. http://dx.doi.org/10.1142/s0129055x96000408.

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Two differential calculi are developed on an algebra generalizing the usual q-oscillator algebra and involving three generators and three parameters. They are shown to be invariant under the same quantum group that is extended to a ten-generator Hopf algebra. We discuss the special case where it reduces to a deformation of the invariance group of the Weyl-Heisenberg algebra for which we prove the existence of a constraint between the values of the parameters.

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16

Peng, Gang, Zhanqing Chen, and Jiarui Chen. "Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method." Advances in Civil Engineering 2018 (September 26, 2018): 1–6. http://dx.doi.org/10.1155/2018/1472840.

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The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so as to derive a new meshless algorithm formula based on the fractional calculus of the generalized Kelvin model. By using the MTS815.02 hydraulic servo rock mechanics test system, the creep test of mudstones is carried out, and the related data of the creep process were obtained. Based on the generalized Kelvin model of fractional calculus, the related creep parameters of the argillaceous sandstone under compression were fitted. The results showed that the solution of the generalized Kelvin model based on fractional calculus was greatly consistent with the numerical method solution. Meanwhile, the meshless algorithm based on fractional calculus had a favorable stability and accuracy.

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17

Promyslov, Vitaly, and Kirill Semenkov. "Non-Statistical Method for Validation the Time Characteristics of Digital Control Systems with a Cyclic Processing Algorithm." Mathematics 9, no. 15 (July 22, 2021): 1732. http://dx.doi.org/10.3390/math9151732.

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The paper discusses the problem of performance and timing parameters with respect to the validation of digital instrumentation and control systems (I&C). Statistical methods often implicitly assume that the probability distribution law of the estimated parameters is close to normal. Thus, the confidence intervals for the parameter are determined on the grounds of this assumption. However, we encountered cases when the delay distribution law in I&C is not normal. In these cases, we used the non-statistical network calculus method for time parameters estimation. The network calculus method is well elaborated for lossless digital system models with seamless processing algorithm depending only on data volume. We consider the extension of the method to the case of I&C systems with considerable changes in the data flow and content-dependent processing disciplines. The model is restricted to systems with cyclic processing algorithms and fast network connections. Network calculus describes the data flow and system parameters in terms of flow envelopes and service curves that are generally unknown in advance. In this paper, we define equations that allow the calculation of these characteristics from experimental data. The correspondence of the Network Calculus and classical statistical estimation methods is discussed. Additionally, we give an example of model application to a real I&C system.

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18

Mohammed, Maher B., and Maha Sh Mahmood. "Assessment of Dental Calculus, Plaque and GingivalInflammation in Patients with Urinary Stone." Journal of Baghdad College of Dentistry 31, no. 1 (March 15, 2019): 14–18. http://dx.doi.org/10.26477/jbcd.v31i1.2572.

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Background: Dental calculus is mineralized dental plaque formed on teeth and dental prosthesis surfaces in the oral cavity. Urinary stone is a crystal aggregation formed in urinary system due to minerals saturation present in urine. The structure of dental calculus is similar to that of urinary stone. Objective: To assess oral hygiene and gingival status in patients with urinary stone. And compared with healthy subjects. Patients and Methods: Sixty participants, 25-40 years, were involved in this study who were divided into study and control group. The study group involved patients with urinary stone while the control group involved healthy subjects. Clinical parameters including plaque, calculus and gingival indices were recorded for all participants. The correlation between the recorded clinical parameters was estimated. Results: The study group mean (±SD) plaque (1.435±0.499), gingival (0.995±0.288) and calculus (1.28 ±0.66) indices were found to be significantly high compared with control group(0.868±0.265), (0.602±0.265) (0.501±0.457 ) respectively. The formed calculus was positively associated with accumulated plaque (r: 0.608, p < 0.05) and gingival inflammation(r: 0.612, p < 0.05). Conclusion: Urinary stone patients were associated with more plaque and calculus accumulation, and had worse gingival inflammation compared to healthy participants. Thus, they need to be more aware of their gingival health status and improved preventive care of oral health.

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19

Ferreira, Larissa A., Diogo M. Sapata, Maria G. A. Provenzano, Roberto M. Hayacibara, and Adilson L. Ramos. "Periodontal parameters of two types of 3 x 3 orthodontic retainer: a longitudinal study." Dental Press Journal of Orthodontics 24, no. 3 (June 2019): 64–70. http://dx.doi.org/10.1590/2177-6709.24.3.064-070.oar.

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ABSTRACT Introduction: bonded fixed retainers are often used to stabilize the results obtained with the orthodontic treatment. It is important that they do not prejudice dental health, as they will be used for a long period. Objective: The purpose of the present study was to compare periodontal indexes between two types of bonded fixed retainers, conventional 3 x 3 plain retainer (0.8-mm orthodontic wire, bonded to the canines only) and a manufactured braided retainer (0.2 x 0.7-mm stainless steel wire, bonded to all anterior teeth) after use. Methods: a test group of 15 volunteers (aged from 18 to 25 years) used both the conventional retainer and braided retainer for six months. A randomized longitudinal study design, with a two week washout interval, was applied. The dental plaque index, gingival index and dental calculus index were evaluated. Furthermore, the calculus accumulated along the retainer wire was measured and all patients answered a questionnaire about the use, acceptance and comfort of both types of retainers. Results: the scores for plaque and gingival indexes were higher for the braided retainer (p< 0.05) on the lingual and proximal surfaces. The same occurred with the calculus index on the lingual surfaces (p< 0.05). The calculus index along wire was higher for the braided retainer (p< 0.05). All patients preferred the conventional retainer, and said that it was also more comfortable to use. Conclusion: it was concluded that the conventional retainer showed better periodontal indexes than the braided type.

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20

Deppman, Airton. "Thermofractals, Non-Additive Entropy, and q-Calculus." Physics 3, no. 2 (May 4, 2021): 290–301. http://dx.doi.org/10.3390/physics3020021.

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Non-additive entropy is obtained through the thermodynamic description of a system with a fractal structure in its energy-momentum space, called a thermofractal. The entropic parameter, q, is determined in terms of the fractal structure parameters. The characteristics of the thermofractals are determined by two parameters associated with the number of degrees of freedom of the fractal structure and the scale. The parameter q, of non-extensive thermodynamics, has a physical meaning related to the number of degrees of freedom of the thermofractal. The two types of thermofractals are distinguished by the value of q>1 or q<1. Studying the group of transformations of the fractal system, we identify three different classes of transformations and their mathematical expressions. For one class of transformations of thermofractals, the group is isomorphic with q-calculus. Another class of transformations led to new mathematical expressions that extended the deformed q-algebra. Finally, we comment regarding the applications of the results obtained here for different areas such as QCD and scale-free networks.

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21

Djordjevic, Djordje, Dusan Petkovic, and Darko Zivkovic. "The appliance of interval calculus in estimation of plate deflection by solving Poisson's bisquared partial differential equation." Facta universitatis - series: Architecture and Civil Engineering 6, no. 2 (2008): 207–20. http://dx.doi.org/10.2298/fuace0802207d.

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The work analyzed the appliance of interval calculus connected to estimation of elements deflection done by reinforced concrete. The simply supported reinforced concrete plate was taken as an example. The plate was loaded by load per unit area. Knowing that there are several parameters that influence the plate deflection, we showed the calculus where the mentioned parameters were given at a certain interval. The results (the final values of deflection) we also got in the form of intervals so it was possible to follow the direct influence of a change of one or more entering parameters on deflection values by using one model and one caculus.

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22

Luchko, Yuri. "The Four-Parameters Wright Function of the Second kind and its Applications in FC." Mathematics 8, no. 6 (June 12, 2020): 970. http://dx.doi.org/10.3390/math8060970.

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In this survey paper, we present both some basic properties of the four-parameters Wright function and its applications in Fractional Calculus. For applications in Fractional Calculus, the four-parameters Wright function of the second kind is especially important. In the paper, three case studies illustrating a wide spectrum of its applications are presented. The first case study deals with the scale-invariant solutions to a one-dimensional time-fractional diffusion-wave equation that can be represented in terms of the Wright function of the second kind and the four-parameters Wright function of the second kind. In the second case study, we consider a subordination formula for the solutions to a multi-dimensional space-time-fractional diffusion equation with different orders of the fractional derivatives. The kernel of the subordination integral is a special case of the four-parameters Wright function of the second kind. Finally, in the third case study, we shortly present an application of an operational calculus for a composed Erdélyi-Kober fractional operator for solving some initial-value problems for the fractional differential equations with the left- and right-hand sided Erdélyi-Kober fractional derivatives. In particular, we present an example with an explicit solution in terms of the four-parameters Wright function of the second kind.

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23

Cavalcanti, Ana, Augusto Sampaio, and Jim Woodcock. "An inconsistency in procedures, parameters, and substitution in the refinement calculus." Science of Computer Programming 33, no. 1 (January 1999): 87–96. http://dx.doi.org/10.1016/s0167-6423(97)00015-4.

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24

Machado, J. A. Tenreiro, and António M. Lopes. "Ranking the scientific output of researchers in fractional calculus." Fractional Calculus and Applied Analysis 22, no. 1 (February 25, 2019): 11–26. http://dx.doi.org/10.1515/fca-2019-0002.

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Abstract This paper analyses the citation profiles (CP) of 130 researchers in fractional calculus. In a first phase, the Canberra distance is used to measure the similarities between the researchers’ CP, and the multidimensional scaling technique (MDS) is adopted for processing and visualizing the information. In a second phase, the gamma probability distribution is used to fit the normalized CP and the gamma parameters are used to characterize the researchers. The MDS results and the gamma distribution parameters are represented graphically in 2- and 3-dimensional locus depicting the relative positions of the researchers.

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25

Fernandez, Arran, and Iftikhar Husain. "Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus." Fractal and Fractional 4, no. 3 (September 12, 2020): 45. http://dx.doi.org/10.3390/fractalfract4030045.

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Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations. Here we propose a modification of the usual Mittag-Leffler functions of one, two, or three parameters, which is ideally suited for extending certain fractional-calculus operators into the complex plane. Complex analysis has been underused in combination with fractional calculus, especially with newly developed operators like those with Mittag-Leffler kernels. Here we show the natural analytic continuations of these operators using the modified Mittag-Leffler functions defined in this paper.

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26

JAY, BARRY, and DELIA KESNER. "First-class patterns." Journal of Functional Programming 19, no. 2 (March 2009): 191–225. http://dx.doi.org/10.1017/s0956796808007144.

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AbstractPure pattern calculus supports pattern-matching functions in which patterns are first-class citizens that can be passed as parameters, evaluated and returned as results. This new expressive power supports two new forms of polymorphism. Path polymorphism allows recursive functions to traverse arbitrary data structures. Pattern polymorphism allows patterns to be treated as parameters which may be collected from various sources or generated from training data. A general framework for pattern calculi is developed. It supports a proof of confluence that is parameterised by the nature of the matching algorithm, suitable for the pure pattern calculus and all other known pattern calculi.

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27

Clarke, DE, M. Kelman, and N. Perkins. "Effectiveness of a Vegetable Dental Chew on Periodontal Disease Parameters in Toy Breed Dogs." Journal of Veterinary Dentistry 28, no. 4 (December 2011): 230–35. http://dx.doi.org/10.1177/089875641102800403.

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Sixteen toy breed dogs completed a parallel, 70-day two-period, cross-over design clinical study to determine the effect of a vegetable dental chew on gingivitis, halitosis, plaque, and calculus accumulations. The dogs were randomly assigned into two groups. During one study period the dogs were fed a non-dental dry diet only and during the second study period were fed the same dry diet supplemented by the daily addition of a vegetable dental chew. Daily administration of the dental chew was shown to reduce halitosis, as well as, significantly reduce gingivitis, plaque and calculus accumulation and therefore may play a significant role in the improvement of canine oral health over the long-term.

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28

Tian, Kelei, Yanyan Ge, and Xiaoming Zhu. "The q-deformed mKP hierarchy with two parameters." Modern Physics Letters B 32, no. 16 (June 5, 2018): 1850170. http://dx.doi.org/10.1142/s0217984918501701.

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In this paper, with the help of the biparametric quantum calculus we construct the Sato theory on the q-deformation modified Kadomtsev–Petviashvili hierarchy with two parameters (qp-mKP), which is a new deformation of classical mKP hierarchy. The Lax equation and dressing operator of qp-mKP hierarchy are derived. By considering the M operator and [Formula: see text] operator, the additional symmetry of qp-mKP hierarchy is obtained.

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29

HAYES, IAN, ROBERT COLVIN, DAVID HEMER, PAUL STROOPER, and RAY NICKSON. "A refinement calculus for logic programs." Theory and Practice of Logic Programming 2, no. 4-5 (July 2002): 425–60. http://dx.doi.org/10.1017/s1471068402001448.

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Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.

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30

Yang, Ningning, Chaojun Wu, Rong Jia, and Chongxin Liu. "Modeling and Characteristics Analysis for a Buck-Boost Converter in Pseudo-Continuous Conduction Mode Based on Fractional Calculus." Mathematical Problems in Engineering 2016 (February 3, 2016): 1–11. http://dx.doi.org/10.1155/2016/6835910.

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In recent days, fractional calculus (FC) has been accepted as a novel modeling tool that can extend the descriptive power of the traditional calculus. Fractional-order descriptiveness can increase the flexibility and degrees of freedom of the model by means of fractional parameters. Based on the fact that real capacitors and inductors are “intrinsic” fractional order, fractional calculus is introduced into the modeling process to establish a fractional-order state-space averaging model of the Buck-Boost converter in pseudo-continuous conduction mode (PCCM). Orders of the model are considered as extra parameters, and these parameters have significant influences on the performance of the model. The inductor current, the inductor current ripple, the amplitude of the output voltage, and the transfer functions of the fractional-order model are all related to orders. The contrast simulation experiments are conducted to investigate the performance of integer-order and fractional-order Buck-Boost converters in PCCM. Results of numerical and circuit simulations demonstrate that the proposed theoretical analysis is effective; the fractional-order model of the Buck-Boost converter in PCCM has certain theoretical and practical significance for modeling and performance analysis of other electrical or electronic equipment.

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31

Gengler, William R., Bruce N. Kunkle, Davida Romano, and Diane Larsen. "Evaluation of a Barrier Dental Sealant in Dogs." Journal of Veterinary Dentistry 22, no. 3 (September 2005): 157–59. http://dx.doi.org/10.1177/089875640502200302.

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A study was conducted in 40 healthy, randomly selected, client-owned, mixed and purebred dogs to assess the efficacy of a barrier dental sealant. All dogs showed evidence of dental plaque, calculus, or gingivitis. The dental sealant was applied to one side of the mouth following a professional teeth cleaning procedure and reapplied weekly for 8-weeks following the cleaning procedure. Dental parameters evaluated included plaque, calculus, gingivitis, and gingival bleeding indices. A statistically significant difference was detected between treated and untreated teeth compared with baseline values for plaque and calculus at weeks 4 and 8, gingivitis at week 4, and gingival bleeding time at week 8. A professional teeth cleaning procedure followed by a single application of the barrier dental sealant and weekly reapplication performed by a veterinarian or veterinary technician provided significant improvement in plaque and calculus indices during an 8-week period.

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32

Popa, Constantin, Mihaela Florentina Duţu, Luminiţa Voiculescu, Alina Ovanisof, and Maria Dragomir. "Kinematic Study of Industrial Robots." Applied Mechanics and Materials 762 (May 2015): 267–70. http://dx.doi.org/10.4028/www.scientific.net/amm.762.267.

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The efficiency of the technological operations executed by robots depends on how their kinematic parameters were calculated. This paper presents the exactly calculus of the robots kinematics parameters. As the algorithm has a substantial number of operations, it is necessary to use the computer.

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33

Saukova, Y. N., and M. A. Hundzina. "Tensor Calculus in Digital Colorimetry." Devices and Methods of Measurements 13, no. 3 (October 24, 2022): 216–27. http://dx.doi.org/10.21122/2220-9506-2022-13-3-216-227.

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Any object can have many implementations in the form of digital images and any digital image can be processed many times increasing or decreasing accuracy and reliability. Digital colorimetry faces the need to work out issues of ensuring accuracy, metrological traceability and reliability. The purpose of this work was to generalize approaches to the description of multidimensional quantized spaces and show the possibilities of their adaptation to digital colorimetry. This approach will minimize the private and global risks in measurements.For color identification digital colorimetry uses standard color models and spaces. Most of them are empirical and are improved during the transition from standard to real observation conditions taking into account the phenomena of vision and the age of observers. From the point of view of measurement, a digital image can be represented by a combinatorial model of an information and measurement channel with the appearance of the phenomenon of a color covariance hypercube requiring a significant amount of memory for data storage and processing. The transition from the covariance hypercube to high-dimensional matrices and tensors of the first, second and higher ranks provides the prospect of optimizing the color parameters of a digital image by the criterion of information entropy.Tensor calculus provides opportunities for expanding the dynamic range in color measurements describing multidimensional vector fields and quantized spaces with indexing tensors and decomposing them into matrices of low orders.The proposed complex approach based on tensor calculus. According to this approach the color space is a set of directed vector fields undergoing sampling, quantization and coding operations. Also it is a dynamic open system exchanging information with the environment at a given level and to identify color with specified levels of accuracy, reliability, uncertainty and entropy.

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Promyslov, Vitaly, and Kirill Semenkov. "The Approaches for the Estimation of Control System Parameters in “Network Calculus”." IFAC-PapersOnLine 54, no. 1 (2021): 954–58. http://dx.doi.org/10.1016/j.ifacol.2021.08.113.

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TOKUNAGA, Shuji, Mitsuo OHKAWA, Hidekazu YAMAMOTO, Mitsuhiro TAKASHIMA, and Haruo HISAZUMI. "Calculus Pyonephrosis due to Candida albicans with Special Reference to Serodiagnostic Parameters." Journal of the Japanese Association for Infectious Diseases 66, no. 6 (1992): 786–89. http://dx.doi.org/10.11150/kansenshogakuzasshi1970.66.786.

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36

Arnold, Ludwig, and Peter Imkeller. "Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory." Stochastic Processes and their Applications 62, no. 1 (March 1996): 19–54. http://dx.doi.org/10.1016/0304-4149(95)00081-x.

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Atanackovic, Teodor M., and Stevan Pilipovic. "Zener Model with General Fractional Calculus: Thermodynamical Restrictions." Fractal and Fractional 6, no. 10 (October 21, 2022): 617. http://dx.doi.org/10.3390/fractalfract6100617.

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We studied a Zener-type model of a viscoelastic body within the context of general fractional calculus and derived restrictions on coefficients that follow from the dissipation inequality, which is the entropy inequality under isothermal conditions. We showed, for a stress relaxation and a wave propagation, that the restriction that follows from the entropy inequality is sufficient to guarantee the existence and uniqueness of the solution. We presented numerical data related to the solution of a wave equation for several values of parameters.

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Abdelkader, Mahdad, Abdeltif Amrane, Mohamed Hentabli, Salah Hanini, and Maamar Laidi. "A Grey Wolf Optimizer-based Fractional Calculus in Studies on Solar Drying." Kemija u industriji 70, no. 1-2 (2021): 39–47. http://dx.doi.org/10.15255/kui.2020.035.

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In this novel article, a comparative study has been conducted between analytical and fractional solution of Fick’s first- and second-order of diffusion to model the solar drying process of different products and dryers under different operating parameters. Laplace and Laplace’s inverse transform have been used to obtain the solution in function with two parameters: the order index n and the fractional time index α of the above Fick’s laws, and their parameters have been non-linearly optimised using a <i>grey wolf optimisation</i> (GWO) algorithm. The results showed that the anomalous diffusion phenomenon during the drying process is best described by the fractional‐order model. Values obtained using the model MR12 were in better agreement with the experimental data than the values obtained using the other selected models with very acceptable statistical parameters.

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Drozdowski, Grzegorz. "Economic Calculus Qua an Instrument to Support Sustainable Development under Increasing Risk." Journal of Risk and Financial Management 14, no. 1 (January 1, 2021): 15. http://dx.doi.org/10.3390/jrfm14010015.

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Investment decisions in the field of sustainable development should be taken based on an economic calculation, taking into account the analysis of a diverse economic environment. The economic calculus of an enterprise is treated as a kind of way of thinking about the rationality of decisions made by an entrepreneur. In the case of sustainable development, the economic calculus serves as an instrument to support the selection of the investment measure. The result of the economic calculus is based on various types of economic parameters, which are subject to frequent changes and high risk. A risk-based financial account may be of little use in the context of the unpredictability of the forecasted situations. In the article, I attempted to determine the importance of a variable interest rate in the economic calculus of a company as an instrument to support sustainable development. For this purpose, I modified the Net Present Value (NPV) meter, which contains actual (variable) discount rates.

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Djordjevic, Djordje, and Predrag Petronijevic. "The application of interval calculus in estimation of dynamic characteristics of structures." Facta universitatis - series: Architecture and Civil Engineering 10, no. 2 (2012): 223–34. http://dx.doi.org/10.2298/fuace1202223d.

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The paper analyzed application of interval calculus in estimation of dynamic characteristics of linear systems. The eigen periods of oscillation of structures are affected by several parameters: geometrical characteristics of cross sections of members, magnitude of the mass concentrated in the floors and modulus of elasticity of materials. As a numerical example, the frame reinforced concrete structure was taken, for which the mentioned parameters are given in the form interval. The result is also obtained in the form of interval so it is possible to observe the direct effects on the value of the structural oscillation periods by changing one or several parameters.

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41

Rybakov, Vladimir V. "Rules of inference with parameters for intuitionistic logic." Journal of Symbolic Logic 57, no. 3 (September 1992): 912–23. http://dx.doi.org/10.2307/2275439.

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AbstractAn algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed.

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Eversberg, Thomas, Anthony F. J. Moffat, Michael Debruyne, John B. Rice, Nikolai Piskunov, Pierre Bastien, William H. Wehlau, and Olivier Chesneau. "Observing Hot Stars in all Four Stokes Parameters." International Astronomical Union Colloquium 169 (1999): 107–10. http://dx.doi.org/10.1017/s0252921100071840.

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AbstractWe introduce a new polarimeter unit which, mounted at the Cassegrain focus of any telescope and fiber-connected to a fixed CCD spectrograph, is able to measure all Stokes parameters I, Q, U and V photon-noise limited across spectral lines of bright stellar targets and other point sources in a quasi-simultaneous manner. We briefly outline the technical design of the polarimeter unit and the linear algebraic Mueller calculus for obtaining polarization parameters of any point source. In addition, practical limitations of the optical elements are discussed. We present first results obtained with our spectropolarimeter for three prototype hot-star.

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43

Singh, Kuldeep, Pooja Singh, and Gurpreet Oberoi. "Comparative studies between herbal toothpaste (dantkanti) and non-herbal tooth paste." International Journal of Dental Research 4, no. 2 (September 30, 2016): 53. http://dx.doi.org/10.14419/ijdr.v4i2.6633.

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The purpose of the paper is to highlight the advantages of using the herbal tooth paste with that of conventional paste. The approach is to make use of naturally available herbs such as Akarkara (anacyclus pyrethrum), Neem (azadirachta indica), Babool (acacia arabica), Haldi (curcuma longa) etc to make herbal paste. These herbal mixture acts as antimicrobial agents. The clinical study is carried out with three parameters – Debris index, Calculus index and Gingival bleeding index. These parameters were compared over conventional paste. We have carried out studies with 100 people of different age groups ranging from 25 to 50 years covering both men and women. The statistical t-test is carried out between the unpaired two groups of herbal and non-herbal pastes. The results shows that the group – A (herbal) has significantly lower debris, calculus and gingival bleeding index value. The debris index and calculus index have p < 0.001, the oral hygiene index also has the p < 0.001, which is significant and the gingival bleeding index has the p < 0.05.The conclusion is that the herbal Dantkanti toothpaste is more efficient in maintenance of oral hygiene and gum bleeding as compared to the non-herbal toothpaste.

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44

Samayoa, Didier, Andriy Kryvko, Gelasio Velázquez, and Helvio Mollinedo. "Fractal Continuum Calculus of Functions on Euler-Bernoulli Beam." Fractal and Fractional 6, no. 10 (September 29, 2022): 552. http://dx.doi.org/10.3390/fractalfract6100552.

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A new approach for solving the fractal Euler-Bernoulli beam equation is proposed. The mapping of fractal problems in non-differentiable fractals into the corresponding problems for the fractal continuum applying the fractal continuum calculus (FdH3-CC) is carried out. The fractal Euler-Bernoulli beam equation is derived as a generalization using FdH3-CC under analogous assumptions as in the ordinary calculus and then it is solved analytically. To validate the spatial distribution of self-similar beam response, three different classical beams with several fractal parameters are analysed. Some mechanical implications are discussed.

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45

Momenzadeh, Mohammad, Olivia Ada Obi, and Evren Hincal. "A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy." Fractal and Fractional 6, no. 6 (May 26, 2022): 287. http://dx.doi.org/10.3390/fractalfract6060287.

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Our study is based on the modification of a well-known predator-prey equation, or the Lotka–Volterra competition model. That is, a system of differential equations was established for the population of healthy and cancerous cells within the tumor tissue of a patient struggling with cancer. Besides, fractional differentiation remedies the situation by obtaining a meticulous model with more flexible parameters. Furthermore, a specific type of non-Newtonian calculus, bi-geometric calculus, can describe the model in terms of proportions and implies the alternative aspect of a dynamic system. Moreover, fractional operators in bi-geometric calculus are formulated in terms of Hadamard fractional operators. In this article, the development of fractional operators in non-Newtonian calculus was investigated. The model was extended in these criteria, and the existence and uniqueness of the model were considered and guaranteed in the first step by applying the Arzelà–Ascoli. The bi-geometric analogue of the numerical method provided a suitable tool to solve the model approximately. In the end, the visual graphs were obtained by using the MATLAB program.

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Liang, Guishu, and Yulan Yang. "Fractional calculus-based analysis of soil electrical properties." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 2 (November 28, 2019): 279–95. http://dx.doi.org/10.1108/compel-05-2019-0179.

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Purpose This paper aims to analyze soil electrical properties based on fractional calculus theory due to the fact that the frequency dependence of soil electrical parameters at high frequencies exhibits a fractional effect. In addition, for the fractional-order formulation, this paper aims to provide a more accurate numerical algorithm for solving the fractional differential equations. Design/methodology/approach This paper analyzes the frequency-dependence of soil electrical properties based on fractional calculus theory. A collocation method based on the Puiseux series is proposed to solve fractional differential equations. Findings The algorithm proposed in this paper can be used to solve fractional differential equations of arbitrary order, especially for 0.5th-order equations, obtaining accurate numerical solutions. Calculating the impact response of the grounding electrode based on the fractional calculus theory can obtain a more accurate result. Originality/value This paper proposes an algorithm for solving fractional differential equations of arbitrary order, especially for 0.5th-order equations. Using fractional calculus theory to analyze the frequency-dependent effect of soil electrical properties, provides a new idea for ground-related transient calculation.

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Котов and P. Kotov. "Modern aspects of integration of nonresonance differential equations with limited right part functions in problems of electrodynamics and astrophysics." Modeling of systems and processes 7, no. 1 (August 8, 2014): 27–30. http://dx.doi.org/10.12737/4951.

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A constructive approach is offered for integration of nonresonance real differential equations with limited functions in the right part considering the famous foundations of differential and integral calculus of measurable function of diagnosable parameters.

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48

Srivastava, Hari Mohan, Pshtiwan Othman Mohammed, Ohud Almutairi, Artion Kashuri та Y. S. Hamed. "Some Integral Inequalities in 𝒱-Fractional Calculus and Their Applications". Mathematics 10, № 3 (24 січня 2022): 344. http://dx.doi.org/10.3390/math10030344.

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We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving the six parameters truncated Mittag–Leffler function and the Gamma function. In view of these, we obtain some integral inequalities of Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, and Grüss type to the V-fractional calculus.

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Katembo, A. L., and M. V. Shitikova. "Influence of fractional calculus model parameters on nonlinear forced vibrations of suspension bridges." IOP Conference Series: Materials Science and Engineering 489 (March 26, 2019): 012037. http://dx.doi.org/10.1088/1757-899x/489/1/012037.

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50

Nowakowski, Jacek, Piotr Ostalczyk, and Dominik Sankowski. "APPLICATION OF FRACTIONAL CALCULUS FOR MODELLING OF TWO-PHASE GAS/LIQUID FLOW SYSTEM." Informatics Control Measurement in Economy and Environment Protection 7, no. 1 (March 30, 2017): 42–45. http://dx.doi.org/10.5604/01.3001.0010.4580.

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In recent years the use of fractional calculus in control system identification is becoming popular and it has found new applications. The paper presents application of fractional calculus for modelling of two-phase gas/liquid flows in a test rig. The installation consists of three horizontal and vertical measuring segments with different diameters, which allow to investigate flows in a wide range of parameters. Flow components supply is measured/controlled by NI PXI system and a set of flow meters/controllers. The paper presents model of the two-phase flow in the above described installation, which leads to precise and accurate flow mathematical model. The main goal of the flow model is to describe steady flow parameters, especially the flow fractions, or type of the flow. The model describes flows more accurately, that classical second order system model.

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