SOLUTION OF EQUATIONS AND INEQUALITIES CONTAINING THE SUM OF MODULES

2020 ◽  
Author(s):  
Маирбек Сулейманович Бичегкуев ◽  
Эльбрус Георгиевич Олисаев
Keyword(s):  
Standard Method ◽  
Graphical Method ◽  
Equivalent System ◽  
Standard Methods ◽  
Solution Of Equations ◽  
Solving Equations

В работе приводится нестандартный метод решения уравнений и неравенств, содержащих сумму модулей, - метод перехода к равносильной системе или совокупности уравнений и неравенств. Это дает более рациональное и короткое решение рассматриваемых задач по сравнению со стандартными способами - методом последовательного раскрытия модулей или графическим методом. The paper presents a non-standard method for solving equations and inequalities containing the sum of modules - a method of transition to an equivalent system or set of equations and inequalities. This gives a more rational and shorter solution to the problems under consideration in comparison with standard methods - the method of sequential expansion of modules or the graphical method.

scholarly journals Microscopy as a Reliable Tool for the Evaluation of Marine Fuels Stability

Paliva ◽  
2020 ◽  
pp. 60-65
Author(s):  
Aleš Vráblík ◽  
Karolína Jaklová ◽  
Nikola Bringlerová ◽  
Dominik Schlehöfer ◽  
Radek Černý
Keyword(s):  
Standard Method ◽  
Deep Sea ◽  
Maximum Level ◽  
Suitable Method ◽  
Stability Testing ◽  
Fast Evaluation ◽  
Standard Methods ◽  
The Stability ◽  
In The Beginning ◽  
Total Sediment

The stability of marine fuels is traditionally a very hot topic, especially in the beginning of so-called sulphur cap. The sulphur cap is the process of reducing the maximum level of sulphur content (from 3.5 to 0.5 wt%) in marine fuels, which are being used on deep sea from the first of January 2020. After this change, the large amount of marine fuels will be produced as a mixture of two or more components to achieve required sulphur level. Higher amounts of cutter stocks will increase the likelihood of decreased stability or compatibility of the marine fuels. Therefore, a reliable stability tests or their combination will be very important for marine fuels evaluation. However, only total sediment after aging is defined as a standard method according to ISO 8217 for stability testing. This method is not suitable for all the analysed marine fuels, so we verified using of microscopy for this type of evaluation. The set of marine fuels samples was tested using microscopy, results were processed and correlated with other selected qualitative parameters. The microscopy was evaluated as a suitable method for testing of marine fuels stability. This method could be used for very fast evaluation in industrial as well as research laboratories in combination with standard methods.

scholarly journals APPLICATION OF INVARIANCE PROPERTIES IN PROBLEMS DEPENDING ON THE PARAMETER

2020 ◽  
Vol 70 (2) ◽  
pp. 47-52
Author(s):  
О.D. Apyshev ◽  
◽  
R.О. Nurkanova ◽  
F.S. Аmenova ◽  
◽  
...  
Keyword(s):  
Elementary Mathematics ◽  
Sufficient Conditions ◽  
Solutions To Equations ◽  
Systems Of Equations ◽  
Invariance Properties ◽  
Solution Of Equations ◽  
Single Solution ◽  
Solving Equations ◽  
Necessary And Sufficient ◽  
Invariant Properties

In this paper, we comprehensively consider the problems that depend on the parameter. The necessary and sufficient conditions for the existence of a unique solution of equations and systems of equations that depend on the parameter are investigated. Finding solutions to equations and systems of equations that depend on parameters is one of the most difficult areas of elementary mathematics. To solve them, you need to find ways that require special logical thinking, which must satisfy some additional conditions, for example, to determine a single solution, a solution in a set of all possible values of unknowns, cases when all the solutions of one system are solutions of another, and so on. One of these cases is the use of invariant properties. The article uses various examples of using invariant properties of transformations to consider methods and techniques for solving equations and systems of equations that depend on a single parameter. As a result, due to the presence of invariant properties of transformations, we see that the desired solution is found quickly and easily.

The solution of equations by iteration

1955 ◽  
Vol 51 (1) ◽  
pp. 41-43 ◽  
Author(s):  
W. A. Coppel
Keyword(s):  
Very Old ◽  
Solution Of Equations ◽  
Solving Equations ◽  
Definition Of ◽  
General Conditions

The method of solving equations by iteration is very old and is discussed in many well-known books. But conditions for its validity have never been properly formulated. In the first place, it is necessary to know that the method will not carry us outside the domain of definition of our functions, and that the ‘approximations’ will not converge to something which is not a solution of the equations. These difficulties are easily forestalled; it is more difficult to ensure that the process really will converge. Our object will be to find the most general conditions under which we can set off with the certainty that we will ultimately arrive at a root, in the case of one equation with one unknown.

An Integrated Parallelizable Algorithm for Computer Motion Simulation of Large-Sized Bio-Molecular Structures

2017 ◽  
Author(s):  
Shanzhong (Shawn) Duan
Keyword(s):  
Fast Multipole Method ◽  
Equations Of Motion ◽  
Molecular Structures ◽  
Motion Simulation ◽  
Fast Multipole ◽  
Molecular Method ◽  
Simulation Procedure ◽  
Solution Of Equations ◽  
Multipole Method ◽  
Solving Equations

In this paper, an integrated parallelizable algorithm is presented for computer simulation of dynamics of multibody molecular structures in polymers and biopolymers. The algorithm is developed according to an integrated O(N) simulation procedure developed by the author for calculating interatomic forces and forming/solving equations of motion for large-sized bio-molecular structures. Specifically, the simulation procedure is created via a proper integration between a parallelizable multibody molecular simulation method (PMMM) produced by the author and a parallelizable fast multipole method (PFMM). PFMM is utilized for calculation of atomic forces such as Van der Waals and Coulomb attractions between the atomics in the molecular structures. The parallelizable multibody molecular method is used for forming/solving equations of motion of large-sized molecular structures in polymers and biopolymers. Currently, the calculation of interatomic forces and formation/solution of equations of motion are treated separately by various procedures. For instance, Fast Multipole Method (FMM) and Cell Multipole Method (CMM) are applied for calculating interatomic forces only. Cartesian Coordinate Method (CCM) and Internal Coordinate Molecular Dynamics Method (ICMM) have been introduced independently for forming/solving equations of motion. Though formation and solution of equations of motions, and atomic force calculations are needed for same molecular structure, there is no direct conversation between two group methods. The proposed algorithm integrates multibody molecular method with fast multipole method in a parallel fashion so that both calculating atomic forces and forming/solving equations of motion can be carried out concurrently in a combined procedure. Computational loads associated with these two simulation tasks then can be divided among sub-chains, and each sub-chain is allocated to a processor on a parallel computing system via a proper integration between PFMM and PMMM. The algorithm can be used on both shared-memory and distributed-memory parallel computational systems. Compared with its counterpart of the integrated O(N) procedure developed by the author before, this algorithm has a computational complexity of O(logN) theoretically (N is number of subsets). The algorithm may find its applications for force calculation and motion simulation associated with large-sized molecular structures of polymers and biopolymers.

scholarly journals Ginsenosides in Commercial Ginseng Products Analyzed by Liquid Chromatography-Tandem Mass Spectrometry

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Linda Uhr ◽  
Yuchun Chen ◽  
Daniel Sit ◽  
Paul C. H. Li
Keyword(s):  
Standard Method ◽  
Internal Standard ◽  
Standard Addition ◽  
Standard Addition Method ◽  
Tandem Mass ◽  
Internal Standard Method ◽  
Addition Method ◽  
Standard Methods ◽  
Chromatography Tandem Mass Spectrometry ◽  
Liquid Chromatography Tandem Mass

Although the LC/MS-MS method has been developed to analyze ginsenosides in ginseng roots, this method has not yet been utilized to quantify ginsenosides in ginseng products. In this paper, an internal standard method by LC/MS-MS was developed to analyze the ginsenosides content in the commercial ginseng products such as the ginseng capsules. We compare the standard addition method and the internal standard methods for the quantification of several ginsenosides (e.g., Rb1, Rb2, Rb3, Rc, Rd, Re, Rg1, and Rg3) in five commercial ginseng capsules. The results showed that the internal standard method is as good as the standard addition method and is a less tedious approach.

On the Solution of Equations in Integers in Preparation for the Passing of Profile Level of the Universal State Exam in Mathematics

2018 ◽  
Vol 6 (4) ◽  
pp. 41-49
Author(s):  
Мария Маскина ◽  
Mariya Maskina ◽  
Светлана Давыдочкина ◽  
Svetlana Davydochkina
Keyword(s):  
Secondary School ◽  
Diophantine Equations ◽  
Solution Of Equations ◽  
Elective Course ◽  
Solving Equations ◽  
Topic Theory ◽  
Selection Of

In the course of mathematics of secondary school it is not provided the consideration of a separate topic “Theory of Diophantine equations”, but such equations are increasingly appearing in the texts of additional entrance tests for technical, physical, mathematical and economic specialties of prestigious universities and in the last task of tests of the profi le level of the exam in mathematics. This material is very scattered in various publications, so for its systematization the authors developed an elective course “The solution of Diophantine equations”. Within the framework of this course, the classification of the main methods of solving equations in integers by elementary means and their adaptation for eleventh grades was carried out. Each of the considered methods of solution is provided with a detailed illustration of the features of its application on examples and a selection of tasks for solution without help of teacher.

Development of the Flavor Profile Analysis Method into a Standard Method for Sensory Analysis of Water

1988 ◽  
Vol 20 (8-9) ◽  
pp. 1-9 ◽  
Author(s):  
I. H. Suffet ◽  
B. M. Brady ◽  
J. H. M. Bartels ◽  
G. Burlingame ◽  
J. Mallevialle ◽  
...  
Keyword(s):  
Standard Method ◽  
Sensory Analysis ◽  
Profile Analysis ◽  
Analysis Method ◽  
Standard Methods ◽  
Odor Quality ◽  
Water And Wastewater ◽  
Flavor Profile Analysis ◽  
Sniffing Technique ◽  
Flavor Profile

The standard methods committee for the 1990 edition of Standard Methods for the Analysis of Water and Wastewater has decided to consider adding a new (provisional) method for the sensory analysis of drinking water - Flavor profile analysis (FPA). A series of issues must be addressed before FPA can become a standard method. The methodology (e.g., temperature of aroma samples, sniffing technique, use of cups vs. flasks, rest intervals between samples, maximum number of samples examined per session) must be standardized. Reference standards for odors must be developed and implemented in order to achieve consistent odor quality descriptions. Development of a flavor wheel can help aid the classification and identification of odors.

A DECISION SUPPORT SYSTEM FOR METHODS OF MEASUREMENT IN CONSTRUCTION PROJECTS

2016 ◽  
Vol 3 (2) ◽  
Author(s):  
Abdelrahman Magdy ◽  
Samer Ezeldin
Keyword(s):  
Decision Support ◽  
Middle East ◽  
Decision Support System ◽  
Support System ◽  
Standard Method ◽  
Real Life ◽  
Building Projects ◽  
Standard Methods ◽  
Method Of Measurement ◽  
Methods Of Measurement

Cost estimation of any construction project depends on issuing the Bill of Quantities which defines and quantifies the work items of any project to be priced. When preparing these bills, a set of guiding rules can be used to ease the preparation which is known as the Method of Measurement. Some institutions issued standard Method of Measurements such as the CESMM, NRM and POMI. Each Method of Measurement has its own characteristics and uses. The use of these standard Methods of Measurement is studied in this paper for the civil and building projects in the Middle East by preparing a questionnaire to be distributed and returned on quantity surveyors in the Middle East. The Results are analyzed and the findings are used to construct a decision support system that automates the process of selection of the suitable standard method of measurement for civil or building projects based on some project parameters. The model was validated by comparing its results with those in real life projects. A conclusion was reached the standard Methods of Measurement are used with POMI having most uses followed by CESMM unlike NRM that has least use so the model can give suitable choice for the Method of Measurement in civil projects unlike building projects since NRM is issued recently and still not used in Middle Eastern projects.

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