scholarly journals COMPUTER TOOLS FOR SOLVING MATHEMATICAL PROBLEMS: A REVIEW

2021 ◽  
pp. 205
Author(s):  
Ivan M. Petković ◽  
Đorđe Herceg
Keyword(s):  
Rapid Development ◽  
Short Review ◽  
Computer Hardware ◽  
Distribution Of Zeros ◽  
Open Problems ◽  
Computer Tools ◽  
Complex Zero ◽  
Computer Visualization ◽  
Roundoff Errors ◽  
Mathematical Problems

The rapid development of digital computer hardware and software has had a dramatic influence on mathematics, and contrary. The advanced hardware and modern sophistical software such as computer visualization, symbolic computation, computerassisted proofs, multi-precision arithmetic and powerful libraries, have provided resolving many open problems, a huge very difficult mathematical problems, and discovering new patterns and relationships, far beyond a human capability. In the first part of the paper we give a short review of some typical mathematical problems solved by computer tools. In the second part we present some new original contributions, such as intriguing consequence of the presence of roundoff errors, distribution of zeros of random polynomials, dynamic study of zero-finding methods, a new three-point family of methods for solving nonlinear equations and two algorithms for the inclusion of a simple complex zero of a polynomial.

scholarly journals Cylindrically symmetric models of gravitational collapse to black holes: A short review

2015 ◽  
Vol 24 (09) ◽  
pp. 1542021 ◽  
Author(s):  
Filipe C. Mena
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Collapse ◽  
A Priori ◽  
Short Review ◽  
Gravitational Energy ◽  
Open Problems ◽  
Trapped Surfaces ◽  
Cylindrically Symmetric ◽  
Survey Results

We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vacuum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching boundary of a particular collapsing region. Along the way, we point out several interesting open problems.

scholarly journals Local and Regional Spatial Analysis of Plant Virus Disease Epidemics with Geographic Information Systems (GIS) and Geostatistics

1998 ◽  
Vol 3 (1) ◽  
pp. 85
Author(s):  
M. R. Nelson ◽  
T. V. Orum
Keyword(s):  
Spatial Analysis ◽  
Plant Virus ◽  
Virus Disease ◽  
Rapid Development ◽  
Plant Diseases ◽  
Computer Hardware ◽  
Virus Diseases ◽  
Agricultural Enterprises ◽  
Disease Epidemics ◽  
User Friendly

Recent advances in personal computer hardware and the rapid development of spatial analysis software that is user-friendly on PC's has provided remarkable new tools for the analysts of plant diseases, particularly ecologically complex virus diseases. Due to the complexity of the disease cycle of the animal-vectored plant virus, these diseases present the most interesting challenges for the application of spatial analysis technology. While traditional quantitative analysis of plant diseases concentrated on within-field spatial analysis, often involving rather arcane mathematical descriptions of pattern, the new spatial analysis tools are most useful at the dimension where many disease epidemics occur, the regional level. The output of many of the programs used in spatial analysis is a highly visual picture of a disease epidemic which has a strong intuitive appeal to managers of agricultural enterprises. Applications by us, thus far, have included tomato, pepper and cotton virus diseases in Arizona. Mexico, California and Pakistan. In addition, this technology has been applied by us to Phytophthora infestans in potato and tomato. Aspergillus flavus in cotton, and regional insect problems of tomato and cotton.

scholarly journals Quantum Information: A Brief Overview and Some Mathematical Aspects

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 273
Author(s):  
Maurice Kibler
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computing ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Short Review ◽  
Mutually Unbiased Bases ◽  
Quantum Bits ◽  
Mathematical Problems ◽  
Classical Information Theory ◽  
Main Ideas

The aim of the present paper is twofold. First, to give the main ideas behind quantum computing and quantum information, a field based on quantum-mechanical phenomena. Therefore, a short review is devoted to (i) quantum bits or qubits (and more generally qudits), the analogues of the usual bits 0 and 1 of the classical information theory, and to (ii) two characteristics of quantum mechanics, namely, linearity, which manifests itself through the superposition of qubits and the action of unitary operators on qubits, and entanglement of certain multi-qubit states, a resource that is specific to quantum mechanics. A, second, focus is on some mathematical problems related to the so-called mutually unbiased bases used in quantum computing and quantum information processing. In this direction, the construction of mutually unbiased bases is presented via two distinct approaches: one based on the group SU(2) and the other on Galois fields and Galois rings.

scholarly journals Structure-preserving deep learning

2021 ◽  
pp. 1-49
Author(s):  
E. CELLEDONI ◽  
M. J. EHRHARDT ◽  
C. ETMANN ◽  
R. I. MCLACHLAN ◽  
B. OWREN ◽  
...  
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Large Scale ◽  
Computational Effort ◽  
Model Complexity ◽  
Future Research ◽  
Learning Methods ◽  
Open Problems ◽  
Mathematical Problems ◽  
Made In

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems involved in applying deep learning: most deep learning methods require the solution of hard optimisation problems, and a good understanding of the trade-off between computational effort, amount of data and model complexity is required to successfully design a deep learning approach for a given problem.. A large amount of progress made in deep learning has been based on heuristic explorations, but there is a growing effort to mathematically understand the structure in existing deep learning methods and to systematically design new deep learning methods to preserve certain types of structure in deep learning. In this article, we review a number of these directions: some deep neural networks can be understood as discretisations of dynamical systems, neural networks can be designed to have desirable properties such as invertibility or group equivariance and new algorithmic frameworks based on conformal Hamiltonian systems and Riemannian manifolds to solve the optimisation problems have been proposed. We conclude our review of each of these topics by discussing some open problems that we consider to be interesting directions for future research.

scholarly journals Periphery Dichotomy and its Investigation by GIS Methods

2016 ◽  
Vol 10 (3-4) ◽  
pp. 131-136
Author(s):  
János Pénzes
Keyword(s):  
Computer Technology ◽  
Rapid Development ◽  
Human Geography ◽  
Regional Science ◽  
Computer Tools ◽  
Gis Tools ◽  
Spatial Parameters ◽  
Peripheral Areas ◽  
Gis Methods ◽  
Definition Of

Centre-periphery dichotomy can be regarded as one of the crucial issues in human geography and regional science. The definition of periphery is far from unambiguous due to its relative expression and its content. This is the reason why can significant number of studies be found focusing on the delimitation of central and peripheral areas. The revolution of computer technology and the rapid development of GIS cause the more and more extended usage of these techniques in the human geography as well. These related studies were categorised by their approaches – namely the locational or developmental centreperiphery concepts – and their GIS tools. Application of spatial parameters with extended datasets and complex GIS based calculations mean the most precise and complicated use of GIS and computer tools in the delimitation of peripheral (and central) areas.

scholarly journals STRUCTURAL AND DESIGN SPECIFICS OF SPACE GRID SYSTEMS

2017 ◽  
Vol 16 (6) ◽  
pp. 475-484 ◽  
Author(s):  
G. M. Gasii
Keyword(s):  
Rapid Development ◽  
Experimental Studies ◽  
Physical And Mechanical Properties ◽  
Short Review ◽  
Theoretical Research ◽  
Software Systems ◽  
Materials Development ◽  
Grid Systems ◽  
Advantages And Disadvantages ◽  
Space Grid

The aim of the study is to identify main trends in the development of space grid structures. In order to reach the purpose it is necessary to conduct a review of the known structural concepts, nodal connections and specifics of the space grid structures and to make conclusions on feasibility improvement of the considered structural concepts that make it possible to develop new solutions without disadvantages residing in the analogues. Analysis of papers written by foreign and national scientists and devoted to theoretical, numerical and experimental studies of stress-strain state, influence of different factors on it and geometrical optimization and designing of space grid structures has been conducted in order to achieve the objectives. Space grid structures and, in particular, flat double-layer grid and most frequent nodes have been studied in the paper. The paper contains a short review of the history on development of space grid structures. It has been found that a rapid development of structural designs was caused by scientific and technical progress and, in particular, improvement of physical and mechanical properties of materials, development of calculation methods, application of software systems for simulating behavior of the structure under load, which significantly increased the calculation accuracy and reduced complexity of design. It has been also established that main parameters that have influence on effectiveness of a structural design are geometric dimensions of its modular elements, ratio of its depth to the span. The world experience on development of connection components has been studied in the paper. The paper presents general classification of nodal connections. Main advantages and disadvantages of existing space grid structures are highlighted and it allows to determine possible methods for their improvement. Theoretical research has permitted to establish that the main direction of spatial grid structures improvement consists in development of new node connection types. Several methods for node improvement have been proposed while taking into account the obtained results.

scholarly journals Display of cryptocurrency in accounting

2021 ◽  
pp. 13-22
Author(s):  
Andrii Makurin
Keyword(s):  
Technological Development ◽  
Rapid Development ◽  
Point Of View ◽  
Intangible Asset ◽  
Accounting System ◽  
Mining Equipment ◽  
Virtual Currency ◽  
Mathematical Problems ◽  
The Cost ◽  
Digital Assets

The purpose of the research to determine the main features of the use of cryptocurrency and its identification as an object in the account. A comparative description of cryptocurrencies, electronic money and paper money is given. It has been established that there are no grounds to classify various types of cryptocurrencies in the accounting system as ordinary currencies or assets in a given period of time because they: are not regulated by any jurisdictions; it is not possible to identify the issuer or the specific organization responsible for its issuance; cryptocurrency exists only in the virtual Internet environment. Methods. General scientific methods and approaches, systematic approach, general research methods (analysis, synthesis, generalization, comparison), statistical methods. Results. The list of stages for reflection of activity of the business entity with use of cryptocurrency is offered and considered. The mining process is analysed and the list of cost items for the extraction of new digital coins is highlighted. The variant on reflection in the account of operations with cryptocurrency on accounts of accounting is offered. There are options for reflection in the accounting of cryptocurrency depending on its recognition: virtual goods, intangible assets, financial investments, digital money. To calculate the cost of cryptocurrency obtained by self-extraction, it is necessary to consider the main costs that need to be identified and reflected in the account. In addition to cryptocurrency, you can extract altcoins, lightcoins or convert cryptocurrencies into stablecoins, which cannot be extracted, but can only be purchased. The article presents the main aspects of calculating the cost, which include: the cost of electricity for individuals and legal entities in the country; the cost of the necessary equipment, its depreciation and maintenance, depreciation; residual value at which you can sell old mining equipment; hash – the speed of solving mathematical problems with one or another equipment; network load and production complexity; monetary value or exchange rate of a particular cryptocurrency or digital assets. Practical meaning. Despite all the scientific developments, the issue of accounting for cryptocurrency from the point of view of IFRS is quite debatable. On the one hand, most propose to account for it as a specific intangible asset. Virtual currency is a huge amount of computing power and digital assets. At this stage of technological development of mankind, cryptocurrency is gaining a stable position in the international market. Prospects for further research. Rapid development is causing further capacity growth and interest, but may eventually lead to collapse. However, if the price stability of the cryptocurrency is achieved, it can be used in international transactions, not just for speculative gain. However, this issue will be directly related to the legalization of the new currency and its recognition by central banks as a means of exchange or storage of money. There is a need for further research to understand the basic conditions for the use of digital currency in the payments market.

scholarly journals SEJARAH PERKEMBANGAN INTERNET DAN KEBUTUHAN INFORMASI DALAM DUNIA PENDIDIKAN

Teknologi ◽  
2012 ◽  
Vol 1 (1) ◽  
Author(s):  
Sumargono Sumargono
Keyword(s):  
High Frequency ◽  
Significant Contribution ◽  
Rapid Development ◽  
Science And Technology ◽  
Positive Influence ◽  
Computer Hardware ◽  
The Internet ◽  
Digital World ◽  
Education Science

  ABSTRAK Adanya kemajuan hardware dan software komputer menjadikan  internet sebagai kebutuhan primer dan penting dalam segala bidang, khususnya dunia pendidikan. Saat ini seluruh aspek kehidupan berhubungan dengan dunia digital dan  internet yang membuat pekerjaan menjadi lebih mudah dan cepat, sehingga meningkatkan efektifitas dan efisiensi. Kelebihan lain yang dapat diperoleh dari digitalisasi informasi adalah berupa buku digital. Buku yang berjilid-jilid dapat disimpan dalam bentuk file yang dimuat di sebuah situs. Saat ini internet menjadi kebutuhan primer dalam dunia pendidikan. Dunia pendidikan mulai bergeser dari sekolah/universitas tradisional menjadi sekolah/universitas e-education. Hal ini merupakan pengaruh positif dari informasi online. Berbagai penelitian menunjukkan adanya kontribusi signifikan dari informasi online pendidikan terhadap akselerasi pengembangan IPTEK. Hal ini ditunjukkan dengan tingginya frekwensi rujukan paper ilimiah online dan cepatnya perkembangan bidang bioinformatika yang memanfaatkan internet secara optimal untuk bertukar data dan hasil observasi. Walaupun pada pelaksanaannya masih ada kelemahan dan kendala dalam hal keamanan, hak cipta dan lain-lain, tetapi proses digitalisasi informasi ini merupakan tahap yang harus kita lalui untuk memajukan pendidikan dan riset di Indonesia. Kata kunci: internet, pendidikan, militer, e-education, IPTEK ABSTRACT Advances in computer hardware and software make the internet as a primary need and importance in all fields, especially education. Currently, all aspects of life associated with the digital world and the internet that makes the job easier and faster, thereby increasing the effectiveness and efficiency. Another advantage that can be obtained from the digitization of information is a form of digital books. Volumes of books can be stored in a file that is loaded on a site. Nowadays the Internet becomes a primary need in education. Education began to shift from the school / traditional universities into e-education. This is the positive influence of information online. Various studies suggest a significant contribution of online information to accelerate the development of science and technology education. This is indicated by a high frequency of references online scientific paper and rapid development of  the field of bioinformatics which optimally utilize the Internet to exchange data and observations. Although in practice there are still weaknesses and constraints in terms of security, copyright and other, but the process of digitizing this information is the stage we have to go through to promote education and research in Indonesia. Key words: internet, education, military, e-education, science and technology

Recent Advances in Catalytic Nonenzymatic Kinetic Resolution of Tertiary Alcohols

Synthesis ◽  
2021 ◽  
Author(s):  
Bo Ding ◽  
Qilin Xue ◽  
Shihu Jia ◽  
Hong-Gang Cheng ◽  
Qianghui Zhou
Keyword(s):  
Asymmetric Catalysis ◽  
Kinetic Resolution ◽  
Rapid Development ◽  
Short Review ◽  
Biologically Active ◽  
Metal Catalysis ◽  
Tertiary Alcohols ◽  
Chiral Compounds ◽  
Recent Advances ◽  
Pure Compounds

The kinetic resolution (KR) of racemates is one of the most widely used approaches to access enantiomerically pure compounds. Over the past two decades, catalytic nonenzymatic KR has gained popularity in the field of asymmetric synthesis due to the rapid development of chiral catalysts and ligands in asymmetric catalysis. Chiral tertiary alcohols are prevalent in a variety of natural products, pharmaceuticals, and biologically active chiral compounds. The catalytic nonenzymatic KR of racemic tertiary alcohols is a straightforward strategy to access enantioenriched tertiary alcohols. This short review describes recent advances in catalytic nonenzymatic KR of tertiary alcohols, including organocatalysis and metal catalysis.

Research on the Parameter Model Simulation Based on Computer Simulation Basketball Match

2013 ◽  
Vol 791-793 ◽  
pp. 1203-1207
Author(s):  
Zhi Guo Liu ◽  
Jun Yu Li ◽  
Xiu Li Ren
Keyword(s):  
Computer Simulation ◽  
Software Testing ◽  
Model Simulation ◽  
Rapid Development ◽  
Test Method ◽  
Computer Hardware ◽  
Software Test ◽  
Parallel Test ◽  
Testing Technology ◽  
Virtual Platform

With the development of computer hardware and software, the simulation of computer virtual simulation has been rapid development. The running process of computer simulation platform need to deal with massive data, and in general software testing technology can not meet the requirements. On the basis of this, an application computer virtual platforms parallel test method is proposed. Firstly, this paper gives a brief introduction for the process of computer simulation, and then the testing method can carry out software programming, it will realize the virtual process of serial FIFO buffer and register through reading and writing function. In order to develop basketball virtual platform as an example, the use of Simulink modules in MATLAB compare the serial and parallel testing of two testing methods used by software debugging time. Finally, we find that the parallel test is the best scheme of computer virtual platform software test, to provide theoretical reference for the design of software testing process.

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