Solving multivariate optimisation problems using inequalities

2017 ◽  
Vol 101 (552) ◽  
pp. 412-423
Author(s):  
Stephen Kaczkowski
Keyword(s):  
Everyday Life ◽  
Surface Area ◽  
Minimum Risk ◽  
Personal Problems ◽  
Ticket Price ◽  
Practical Applications ◽  
Mathematical Problems ◽  
Maximum Work ◽  
Work Done ◽  
Everyday Problems

Optimisation problems are among the most practical applications of calculus to everyday life, and a survey of exercises in various calculus textbooks will provide a teacher with many interesting scenarios for framing intriguing questions on this topic. Whether it is finding a container's dimensions that yield the least surface area for a given volume, or finding that ideal movie ticket price which will maximise a theatre's revenue, students can usually relate to these problems. Pólya in his bookPlausible reasoningmakes the following remarks about the attraction of extrema problems:Problems concerned with greatest and least values, or maximum and minimum problems, are more attractive, perhaps, than other mathematical problems of comparable difficulty, and this may be due to a quite primitive reason. Every one of us has his personal problems. We may observe that these problems are very often maximum or minimum problems of a sort. We wish to obtain a certain object at the lowest possible price, or the greatest possible effect with a certain effort, or the maximum work done within a given time and, of course, we wish to run the minimum risk. Mathematical problems on maxima and minima appeal to us, I think, because they idealize our everyday problems. We are even inclined to imagine that Nature acts as we would like to act, obtaining the greatest effect with the least effort [1, p. 121].

scholarly journals Some k-fractional extension of Grüss-type inequalities via generalized Hilfer–Katugampola derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Fractional Integral ◽  
Integral Inequalities ◽  
Derivative Operator ◽  
Practical Applications ◽  
Mathematical Problems ◽  
Grüss Type Inequalities

AbstractIn this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.

scholarly journals USE OF PSYCHOTROPICS IN EVERYDAY LIFE FROM THE PERSPECTIVE OF HEALTH PROFESSIONALS AND PATIENTS: A SYSTEMATIC REVIEW

2017 ◽  
Vol 4 (3) ◽  
pp. 1 ◽  
Author(s):  
Agnes Fonseca Ribeiro Filardi ◽  
VÂnia Eloisa De AraÚjo ◽  
Yone De Almeida Nascimento ◽  
Djenane Ramalho De Oliveira
Keyword(s):  
Systematic Review ◽  
Everyday Life ◽  
Psychotropic Drugs ◽  
Health Professionals ◽  
Inclusion Criteria ◽  
Personal Problems ◽  
Pubmed Central ◽  
Manual Search ◽  
The Social ◽  
Support Mechanisms

The use of psychotropic drugs to treat problems of everyday life is a growing phenomenon in many countries. A systematic review was conducted as a method of synthesis of results of the qualitative primary studies developed to explore the perspective of health professionals and patients regarding the use of psychotropic drugs to overcome personal problems. This systematic review was conducted in the databases Medline (PubMed), Central (Cochrane), Psycoinfo and Lilacs, including gray literature and manual search (june/2015). We identified 581 publications that were evaluated in stages and 26 met the inclusion criteria with a total of 876 participants including health professionals and patients. The doctors showed empathy by prescribing. The health professionals-prescribers and non-prescribers-were concerned about the dependence of patients on the psychotropic and the pressure to prescribe. Patients felt unable to solve their problems and seek medications as a solution. The psychotropics were considered a useful resource to overcome the social problems, existing denial of its side effects as well as the lack of openness and access to other support mechanisms.

Book Review: Personal Problems of Everyday Life

The Family ◽  
1941 ◽  
Vol 22 (8) ◽  
pp. 284-285
Author(s):  
Anna Budd Ware
Keyword(s):  
Everyday Life ◽  
Personal Problems

Theoretical Evaluation of the Maximum Work of Free-Piston Engine Generators

2017 ◽  
Vol 42 (1) ◽  
Author(s):  
Shinji Kojima
Keyword(s):  
Pressure Ratio ◽  
Adjoint Equations ◽  
Brayton Cycle ◽  
Piston Engine ◽  
Theoretical Evaluation ◽  
Free Piston ◽  
Free Piston Engine ◽  
Parametric Studies ◽  
Maximum Work ◽  
Work Done

AbstractUtilizing the adjoint equations that originate from the calculus of variations, we have calculated the maximum thermal efficiency that is theoretically attainable by free-piston engine generators considering the work loss due to friction and Joule heat. Based on the adjoint equations with seven dimensionless parameters, the trajectory of the piston, the histories of the electric current, the work done, and the two kinds of losses have been derived in analytic forms. Using these we have conducted parametric studies for the optimized Otto and Brayton cycles. The smallness of the pressure ratio of the Brayton cycle makes the net work done

Transport in Compounds Containing a Dispersed Second Phase.

1983 ◽  
Vol 24 ◽  
Author(s):  
J. Bruce Wagner
Keyword(s):  
Ionic Conductivity ◽  
Space Charge ◽  
Surface Area ◽  
Double Layer ◽  
Solid Electrolytes ◽  
Volume Ratio ◽  
Ionic Conductor ◽  
Second Phase ◽  
Practical Applications ◽  
Metallic Conductor

ABSTRACTThe introduction of a dispersion of small (≃ 1μ1m) insulating particles into an ionic conductor results in an increase in the ionic conductivity. This behavior is not in accord with classical theory. A number of different examples such as a dispersion of a metallic conductor in a semiconductor, a dispersion of an insulator in a semicondutor, and a dispersion of a metallic conductor in an ionic conductor all yield unusual transport behaviors when the surface area to volume ratio of the dispersoid is large. Under such conditions, a space charge layer or double layer adjacent to the dispersoid must be considered. Practical applications such as solid electrolytes, electrodes, corrosion systems and geological systems were discussed.

scholarly journals Pressure-induced spin crossover in a Prussian Blue analogue

2014 ◽  
Vol 70 (a1) ◽  
pp. C154-C154 ◽  
Author(s):  
Gregory Halder ◽  
Karena Chapman ◽  
Peter Chupas ◽  
Antonio dos Santos
Keyword(s):  
Prussian Blue ◽  
Neutron Source ◽  
Molecular Magnets ◽  
Department Of Energy ◽  
Spallation Neutron Source ◽  
Prussian Blue Analogue ◽  
Practical Applications ◽  
Oak Ridge ◽  
Work Done ◽  
Photon Source

The structural and chemical versatility of functional molecular materials, such as molecular magnets and metal-organic frameworks (MOFs), underlie important technological, industrial, and environmental applications. The extensive structural complexities now well-documented for these systems are likely to be associated with unprecedented pressure-induced behavior compared with the traditional solid state materials more commonly explored under high pressure conditions.1 Furthermore, the typically open (low density, often porous) nature of these materials is likely to induce such phenomena at more moderate pressures, such as may be routinely encountered in practical applications.2,3 Here we report pressure-induced spin-state switching in the Prussian Blue analogue, FePt(CN)6, including in situ Synchrotron (17-BM, Advanced Photon Source) and Neutron (SNAP, Spallation Neutron Source) powder diffraction studies. Work done at Argonne and use of the Advanced Photon Source (APS) was supported by the U.S. Department of Energy under Contract No. DE-AC02-06CH11357. Research at Oak Ridge National Laboratory's Spallation Neutron Source (SNS) was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U. S. Department of Energy.

scholarly journals Plasma-Assisted Three-Dimensional Lightscribe Graphene as High Performance Supercapacitors

2021 ◽  
Author(s):  
Naser Namdar ◽  
Foad Ghasemi ◽  
Zeinab Sanaee
Keyword(s):  
Electrical Conductivity ◽  
Graphene Oxide ◽  
Energy Storage ◽  
Surface Area ◽  
High Performance ◽  
Sulfur Hexafluoride ◽  
Effective Surface Area ◽  
Effective Surface ◽  
Practical Applications ◽  
Sequential Processes

Abstract Graphene-based supercapacitors demonstrate extraordinary energy storage capacity due to their layered structure, large effective surface area, high electrical conductivity and acceptable chemical stability. Herein, reduced graphene oxide (rGO)-based supercapacitors were introduced in a simple, green, fast and inexpensive method. For this purpose, graphene oxide (GO) was synthesized by the modified Hummers’ method and then easily reduced to desired patterns of rGO using a commercial LightScribe DVD drive. In order to increase the effective surface area, as well as the electrical conductivity of rGO layers, oxygen/sulfur hexafluoride plasma was applied to the rGO followed by laser irradiation. By performing such sequential processes, an rGO-based supercapacitor was introduced with a capacitance of about 10.2 F/cm3, which had high stability for more than 1000 consecutive charge-discharge cycles. The fabrication steps of the electrodes were investigated by different analyses such as SEM, TEM, Raman, surface resistance and XPS measurements. Results show that these rGO-based electrodes fabricated by sequential processes are very interesting for practical applications of energy storage.

scholarly journals Conexões entre grafos e matrizes na modelagem de problemas matemáticos

2019 ◽  
Vol 40 ◽  
pp. 183
Author(s):  
Larissa Melchiors Furlan ◽  
Mylena Roehrs ◽  
Glauber Rodrigues de Quadros
Keyword(s):  
Directed Graph ◽  
Real World ◽  
Adjacency Matrix ◽  
Directed Graphs ◽  
The Real ◽  
Mathematical World ◽  
The Everyday ◽  
Mathematical Problems ◽  
Everyday Problems

Graphs theory is very important in the mathematical world as an excellent way of connecting with the real world. By using the theory of directed graphs it is possible to transform many of the everyday problems into mathematical problems, so as to make an exact study in each case. In this work we explore the matrices related to the various types of graphs, such as the vertex matrix, which is associated with a directed graph, and the adjacency matrix. Moreover, matrices of multi-step connections are constructed so as to separate the various blades between the vertices of a directed graph. Then, we will construct some applications of those results in the form of examples.

scholarly journals LAWANG SEWU DALAM SUDUT PANDANG GEOMETRI

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Utari Oktaviani dkk
Keyword(s):  
Data Collection ◽  
Everyday Life ◽  
Real Life ◽  
Historic Buildings ◽  
Historical Buildings ◽  
Geometry Structure ◽  
Mathematical Problems ◽  
Qualitative Descriptive ◽  
The City ◽  
Descriptive Method

<p><em> </em><em>LAWANG SEWU IN GEOMETRY VIEW. Mathematics and culture are two things closely related. But sometimes mathematics is seen as something that is not connected to everyday life. Infactthe environment can be a source of mathematical problems in real life. The environment is one of culture, one of which includes historic buildings. Mathematics in culture is referred to by the term ethnomatematics. Lawang Sewu is one of the historical buildings located in the city of Semarang. The purpose of this research is to know the geometry structure of Lawang SEWU building. This building can be used as a research object with qualitative descriptive method, with data collection using direct observation on research object, interview with speaker, and using library study related to research This. Through research that the authors have done, it can be concluded that Lawang SEWU building has a geometry structure of space, namely cube, beam, Limas, and Octagonal prism.</em></p>

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