scholarly journals On the Comparison of Gauss and Hybrid Methods and their Application to Calculation of Definite Integrals

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Necessary Conditions ◽  
Hybrid Methods ◽  
Definite Integral ◽  
Implicit Methods ◽  
Definite Integrals ◽  
Advantages And Disadvantages ◽  
Chebyshev Method ◽  
Gauss Method ◽  
Gauss Quadrature Formula ◽  
To Receive

As is known there is the wide class of methods for calculation of the definite integrals constructed by the well-known scientists as Newton, Gauss, Chebyshev, Cotes, Simpson, Krylov and etc. It seems that to receive a new result in this area is impossible. The aim of this work is the applied some general form of hybrid methods to computation of definite integral and compares that with the Gauss method. The generalization of the Gauss quadrature formula have been fulfilled in two directions. One of these directions is the using of the implicit methods and the other is the using of the advanced (forward-jumping) methods. Here have compared these methods by shown its advantages and disadvantages in the results of which have recommended to use the implicit method with the special structure. And also are constructed methods, which have applied to calculation of the definite integral with the symmetric bounders. As is known, one of the popular methods for calculation of the definite integrals with the symmetric bounders is the Chebyshev method. Therefore, here have defined some relations between of the above mentioned methods. For the application constructed, here methods are defined the necessary conditions for its convergence. The receive results have illustrated by calculation the values for some model integral using the methods with the degree p  8.

scholarly journals Novel Symmetric Numerical Methods for Solving Symmetric Mathematical Problems

2021 ◽  
Vol 15 ◽  
pp. 1545-1557
Author(s):  
V. R. Ibrahimov ◽  
G.Yu. Mehdiyeva ◽  
Xiao-Guang Yue ◽  
Mohammed K.A. Kaabar ◽  
Samad Noeiaghdam ◽  
...  
Keyword(s):  
Numerical Integration ◽  
Hybrid Methods ◽  
Multistep Methods ◽  
Integration Theory ◽  
Symmetric Methods ◽  
Definite Integrals ◽  
Gauss Method ◽  
Mathematical Problems ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model

The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p<=8 are constructed to solve some problems, and obtained results are compared with other known methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. On the intersection of multistep and hybrid methods have been constructed multistep methods and have been proved that these methods are more exact than others. And also has been shown that, hybrid methods constructed here are more exact than Gauss methods. Noted that constructed here hybrid methods preserves the properties of the Gauss method.

scholarly journals How to Improve Physico-Chemical Properties of Silk Fibroin Materials for Biomedical Applications?—Blending and Cross-Linking of Silk Fibroin—A Review

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1510
Author(s):  
Sylwia Grabska-Zielińska ◽  
Alina Sionkowska
Keyword(s):  
Silk Fibroin ◽  
Biomedical Applications ◽  
Magnetic Particles ◽  
Chemical Properties ◽  
Ternary Mixtures ◽  
Cross Linking ◽  
Advantages And Disadvantages ◽  
Physico Chemical ◽  
Binary And Ternary Mixtures ◽  
To Receive

This review supplies a report on fresh advances in the field of silk fibroin (SF) biopolymer and its blends with biopolymers as new biomaterials. The review also includes a subsection about silk fibroin mixtures with synthetic polymers. Silk fibroin is commonly used to receive biomaterials. However, the materials based on pure polymer present low mechanical parameters, and high enzymatic degradation rate. These properties can be problematic for tissue engineering applications. An increased interest in two- and three-component mixtures and chemically cross-linked materials has been observed due to their improved physico-chemical properties. These materials can be attractive and desirable for both academic, and, industrial attention because they expose improvements in properties required in the biomedical field. The structure, forms, methods of preparation, and some physico-chemical properties of silk fibroin are discussed in this review. Detailed examples are also given from scientific reports and practical experiments. The most common biopolymers: collagen (Coll), chitosan (CTS), alginate (AL), and hyaluronic acid (HA) are discussed as components of silk fibroin-based mixtures. Examples of binary and ternary mixtures, composites with the addition of magnetic particles, hydroxyapatite or titanium dioxide are also included and given. Additionally, the advantages and disadvantages of chemical, physical, and enzymatic cross-linking were demonstrated.

scholarly journals Generalizations and applications of Young’s integral inequality by higher order derivatives

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jun-Qing Wang ◽  
Bai-Ni Guo ◽  
Feng Qi
Keyword(s):  
Differential Geometry ◽  
Integral Inequality ◽  
Higher Order ◽  
Integral Inequalities ◽  
List Type ◽  
Definite Integral ◽  
Exponential Integral ◽  
Definite Integrals ◽  
Logarithmic Integral

Abstract In the paper, the authors generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.

scholarly journals Patient Provider Continuity and Prostate Specific Antigen Testing: Impact of Continuity on Receipt of a Non-recommended Test

2021 ◽  
Vol 8 ◽  
Author(s):  
Arch G. Mainous ◽  
Benjamin J. Rooks ◽  
Elvira S. Mercado ◽  
Peter J. Carek
Keyword(s):  
Prostate Specific Antigen ◽  
Continuity Of Care ◽  
Specific Antigen ◽  
Behavioral Risk ◽  
Psa Test ◽  
Advantages And Disadvantages ◽  
Psa Screening ◽  
Personal Doctor ◽  
Nationally Representative ◽  
To Receive

Background: Continuity of care with a regular physician has been associated with treatment adherence but it is unclear if continuity of care may lead to inappropriate treatments. We assessed the relationship between the receipt of prostate-specific antigen (PSA) screening, a non-recommended test, and having continuity with a single personal doctor.Methods: We analyzed the 2016 and 2018 Behavioral Risk Factor Surveillance System (BRFSS). Responses from men aged 40 and older with no symptoms or family history of prostate cancer were analyzed (unweighted n = 232,548, representing 36,919,766 individuals). Continuity with one doctor was analyzed in relation to discussions of advantages and disadvantages of PSA tests, provider recommendation to receive a test and receipt of a PSA test.Results: 39.5% of men received PSA screening during the time that the test was not recommended. Having a single personal doctor was associated with discussion of both advantages (53.3 vs. 29.7%, p &lt; 0.001) and disadvantages (24.2 vs. 13.5%, p &lt; 0.001) of PSA tests but also a recommendation to receive a PSA test (45.3 vs. 29.3%, p &lt; 0.001). The adjusted odds of receiving a PSA test was higher among those with a single personal doctor compared to those without (OR 2.31; 95% CI, 2.17–2.46).Conclusion: In a nationally representative sample during the time when PSA screening was not recommended by the US Preventive Services Taskforce, having a single personal doctor was associated with both recommendations for the test and receipt of the test. These findings emphasize the importance of the patient physician relationship and the need for evidence-based care.

scholarly journals Definite Integral of Algebraic, Exponential and Hyperbolic Functions Expressed in Terms of Special Functions

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1425
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Closed Form ◽  
Special Function ◽  
Special Functions ◽  
Complex Numbers ◽  
Definite Integral ◽  
Hyperbolic Functions ◽  
Closed Form Solutions ◽  
Definite Integrals ◽  
Arbitrary Complex ◽  
Famous Book

While browsing through the famous book of Bierens de Haan, we came across a table with some very interesting integrals. These integrals also appeared in the book of Gradshteyn and Ryzhik. Derivation of these integrals are not listed in the current literature to best of our knowledge. The derivation of such integrals in the book of Gradshteyn and Ryzhik in terms of closed form solutions is pertinent. We evaluate several of these definite integrals of the form ∫0∞(a+y)k−(a−y)keby−1dy, ∫0∞(a+y)k−(a−y)keby+1dy, ∫0∞(a+y)k−(a−y)ksinh(by)dy and ∫0∞(a+y)k+(a−y)kcosh(by)dy in terms of a special function where k, a and b are arbitrary complex numbers.

DEINSTITUTIONALIZATION OF THE CHILD CARE SYSTEM IN LITHUANIA

2020 ◽  
Vol 11 (4.1) ◽  
pp. 121-131
Author(s):  
Jolanta Pivoriene
Keyword(s):  
Child Care ◽  
Necessary Conditions ◽  
Institutional Care ◽  
Secondary Data ◽  
Community Based ◽  
Political Discourses ◽  
Qualitative Evidence ◽  
To Receive ◽  
Community Based Services ◽  
Care System

The reform of the child care system in Lithuania started with the Ministry of Social Security and Labor approving the Strategic Guidelines for Deinstitutionalization in 2012, followed by the Transition from Institutional Care to Community-Based Services in 2014. The strategic aim of the reform was to create a system including a comprehensive range of services that would enable every child and their family or guardians to receive individual services as well as community assistance according to their needs. The process of transformation of institutional care was designed in two steps: creation of the necessary conditions for the transformation, which took place in 2014 to 2017, and development of infrastructure in the regions, planned for 2017 to 2020, but now extended to 2023. The goal of this article is to discuss the deinstitutionalization process by presenting legal regulations, information about the conceptualization and scope of the project, and evidence based on documents and statistical and secondary data analysis. I will also discuss possible contradictions between analytical and political discourses, and quantitative and qualitative evidence.

scholarly journals VI. On the multiplication of definite integrals

1875 ◽  
Vol 23 (156-163) ◽  
pp. 120-121
Keyword(s):  
Definite Integral ◽  
Definite Integrals ◽  
Straight Lines

The definite integral ∫ y 1 y 0 ∫ x 1 x 0 P dx dy may be considered geometrically as the integral ∫ P dx dy extended over an area bounded by the straight lines whose equations are x = y 1 , x = y 0 , y = x 1 , y = x 0 . Now conceive the axes transformed through an angle of 45°, so that x = ξ/√2 = ƞ/√2, y = ξ/√2 + ƞ/√2; then the equations to the four straight lines become ξ/√2 - ƞ/√2 = y 1 , ξ/√2 - ƞ/√2 = y 0 , ξ/√2 + ƞ/√2 = x 1 , ξ/√2 + ƞ/√2 = x 0 .

scholarly journals STUDY METHODS FOR MONITORING OF TELECOMMUNICATION SYSTEMS

2020 ◽  
Vol 6 (1) ◽  
pp. 143-148
Author(s):  
Mikhail M. Zykin ◽  
Sergey N. Novikov
Keyword(s):  
Hybrid Methods ◽  
Optimal Operation ◽  
Monitoring Method ◽  
Advantages And Disadvantages ◽  
Network State ◽  
Optimal Monitoring ◽  
Telecommunication Systems ◽  
Telecommunications Network ◽  
Routing Tables ◽  
Different Levels

The article describes main steps for centralizing routing table databases. Advantages and disadvantages of databases formed at different levels of centralization are described. Main methods of forming routing tables are described. The advantages and disadvantages of each method are indicated. There are also examples of network protocols that are used to implement a particular method for generating databases about the network state. Possible hybrid methods are identified by combining standard methods for creating databases describing the network state. To ensure optimal operation of the telecommunications network, the optimal monitoring method should be selected based on the degree of centralization and the method for creating a database of routing tables. Depending on the scale of the network and the degree of centralization of its resources, it is needed to choose the best method for monitoring the network.

scholarly journals Artifact Removal Methods in EEG Recordings: A Review

2021 ◽  
Vol 20 ◽  
pp. 35-56
Author(s):  
Mariyadasu Mathe ◽  
Padmaja Mididoddi ◽  
Battula Tirumala Krishna
Keyword(s):  
Wavelet Transform ◽  
Spectrum Analysis ◽  
Hybrid Methods ◽  
Singular Spectrum Analysis ◽  
Discrete Wavelet ◽  
Eeg Signals ◽  
Artifact Removal ◽  
Filtering Method ◽  
Advantages And Disadvantages ◽  
Singular Spectrum

To obtain the correct analysis of electroencephalogram (EEG) signals, non-physiological and physiological artifacts should be removed from EEG signals. This study aims to give an overview on the existing methodology for removing physiological artifacts, e.g., ocular, cardiac, and muscle artifacts. The datasets, simulation platforms, and performance measures of artifact removal methods in previous related research are summarized. The advantages and disadvantages of each technique are discussed, including regression method, filtering method, blind source separation (BSS), wavelet transform (WT), empirical mode decomposition (EMD), singular spectrum analysis (SSA), and independent vector analysis (IVA). Also, the applications of hybrid approaches are presented, including discrete wavelet transform - adaptive filtering method (DWT-AFM), DWT-BSS, EMD-BSS, singular spectrum analysis - adaptive noise canceler (SSA-ANC), SSA-BSS, and EMD-IVA. Finally, a comparative analysis for these existing methods is provided based on their performance and merits. The result shows that hybrid methods can remove the artifacts more effectively than individual methods.

Sign in / Sign up

Export Citation Format

Share Document