scholarly journals Interpolation with Specified Error of a Point Series Belonging to a Monotone Curve

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 493
Author(s):  
Yevhen Havrylenko ◽  
Yuliia Kholodniak ◽  
Serhii Halko ◽  
Oleksandr Vershkov ◽  
Larysa Bondarenko ◽  
...  
Keyword(s):  
Interpolation Error ◽  
Output Section ◽  
Intermediate Point ◽  
Original Curve ◽  
Smooth Contour ◽  
The Absolute ◽  
Special Points ◽  
The Given

The paper addresses the problem of modeling a smooth contour interpolating a point series belonging to a curve containing no special points, which represents the original curve with specified accuracy. The contour is formed within the area of possible location of the parts of the interpolated curve along which the curvature values are monotonously increased or decreased. The absolute interpolation error of the point series is estimated by the width of the area of possible location of the curve. As a result of assigning each intermediate point, the location of two new sections of the curve that lie within the area of the corresponding output section is obtained. When the interpolation error becomes less than the given value, the area of location of the curve is considered to be formed, and the resulting point series is interpolated by a contour that lies within the area. The possibility to shape the contours with arcs of circles specified by characteristics is investigated.

scholarly journals The Structure of the Silumin Coat on Alloy Cast Steels

2012 ◽  
Vol 12 (2) ◽  
pp. 215-220
Author(s):  
T. Szymczak
Keyword(s):  
Phase Structure ◽  
High Speed ◽  
Cast Steel ◽  
Intermetallic Phases ◽  
External Layer ◽  
Cast Steels ◽  
Steel Grades ◽  
The Absolute ◽  
The Given ◽  
Alloy Cast

The Structure of the Silumin Coat on Alloy Cast Steels The work presents the analysis results of the structure of the coat obtained by dipping in silumin AlSi5 of two grades of alloy cast steel: GX6CrNiTi18-10 (LH18N9T) and GX39Cr13 (LH14). The temperature of the silumin bath was 750±5°C, and the hold-up time of the cast steel element τ = 180 s. The absolute thickness of the coat obtained in the given conditions was g = 104 μm on cast steel GX6CrNiTi18-10 and g = 132 μm on GX39Cr13. The obtained coat consisted of three layers of different phase structure. The first layer from the base "g1" was constructed of the phase AlFe including Si and alloy additives of the tested cast steel grades: Cr and Ni (GX6CrNiTi18-10) and Cr (GX39Cr13). The second layer "g1" of intermetallic phases AlFe which also contains Si and Cr crystallizes on it. The last, external layer "g2" of the coat consists of the silumin containing the intermetallic phases AlFeSi which additionally can contain alloy additives of the cast steel. It was shown that there were no carbides on the coat of the tested cast steels which are the component of their microstructure, as it took place in the case of the coat on the high speed steels.

Standardizing 125I Sources and Determining 125I Counting Efficiencies of Well-Type Gamma Counting Systems

1975 ◽  
Vol 21 (3) ◽  
pp. 370-375 ◽  
Author(s):  
Donald L Horrocks
Keyword(s):  
Decay Rate ◽  
Counting Efficiency ◽  
Counting System ◽  
Sample Geometry ◽  
Gamma Counting ◽  
Extended Sources ◽  
The Absolute ◽  
The Given

Abstract I describe the technique for determining the absolute decay rate of any 125I source. The problems of varying counting efficiency, varying sample geometry, and extended sources are discussed. By using the calibrated 125I source, the counting efficiency of the given counting system was obtained.

scholarly journals THE MINIMIZATION OF MOMENTS AND REACTIVE FORCES IN GRILLAGES WITH A GENETIC ALGORITHM

2011 ◽  
Vol 3 (2) ◽  
pp. 56-63
Author(s):  
Rimantas Belevičius ◽  
Darius Mačiūnas ◽  
Dmitrij Šešok
Keyword(s):  
Finite Element ◽  
Bending Moment ◽  
Design Parameters ◽  
Finite Element Program ◽  
One Dimensional ◽  
Absolute Value ◽  
Element Program ◽  
The Absolute ◽  
The One ◽  
The Given

The aim of the article is to report a technology for the optimization of grillage-type foundations seeking for the least possible reactive forces in the piles for a given number of piles and in the absolute value of the bending moments when connecting beams of the grillage. Mathematically, this seems to be the global optimization problem possessing a large number of local minima points. Both goals can be achieved choosing appropriate pile positions under connecting beams; however, these two problems contradict to each other and lead to diff erent schemes for pile placement. Therefore, we suggest using a compromise objective function (to be minimized) that consists of the largest reactive force arising in all piles and that occurring in the absolute value of the bending moment when connecting beams, both with the given weights. Bending moments are calculated at three points of each beam. The design parameters of the problem are positions of the piles. The feasible space of design parameters is determined by two constraints. First, during the optimization process, piles can move only along connecting beams. Therefore, the two-dimensional grillage is “unfolded” to the one-dimensional construct, and supports are allowed to range through this space freely. Second, the minimum allowable distance between two adjacent piles is introduced due to the specific capacities of a pile driver. Also, due to some considerations into the scheme of pile placement, the designer sometimes may introduce immovable supports (usually at the corners of the grillage) that do not participate in the optimization process and always retain their positions. However, such supports hinder to achieve a global solution to a problem and are not treated in this paper. The initial data for the problem are as follows: a geometrical scheme of the grillage, the given number of piles, a cross-section and material data on connecting beams, the minimum possible distance between adjacent supports and loading data given in the form of concentrated loads or trapezoidal distributed loadings. The results of the solution are the required positions of piles. This solution can serve as a pilot project for more detailed design. The entire optimization problem is solved in two steps. First, the grillage is transformed into the one-dimensional construct and the optimizer decides about a routine solution (i.e. the positions of piles in this construct). Second, backward transformation returns pile positions into the two-dimensional grillage and the “black-box” finite element program returns the corresponding objective function value. On the basis of this value, the optimizer predicts new positions of piles etc. The finite element program idealizes connecting beams as beam elements and piles – as mesh nodes of the finite element with a given boundary conditions in the form of vertical and rotational stiff ness. Since the problem may have several tens of design parameters, the only choice for optimization algorithms is using stochastic optimization algorithms. In our case, we use the original elitist real-number genetic algorithm and launch the program sufficient number of times in order to exclude large scattering of results. Three numerical examples are presented for the optimization of 10-pile grillage: when optimizing purely the largest reactive force, purely the largest in the absolute value of the bending moment and both parameters with equal weights.

scholarly journals Extremal Matching Energy and the Largest Matching Root of Complete Multipartite Graphs

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Xiaolin Chen ◽  
Huishu Lian
Keyword(s):  
Split Graph ◽  
Matching Polynomial ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
The Absolute ◽  
Complete Multipartite ◽  
The Given ◽  
Turán Graph

The matching energy ME(G) of a graph G was introduced by Gutman and Wagner, which is defined as the sum of the absolute values of the roots of the matching polynomial m(G,x). The largest matching root λ1(G) is the largest root of the matching polynomial m(G,x). Let Kn1,n2,…,nr denote the complete r-partite graph with order n=n1+n2+…+nr, where r>1. In this paper, we prove that, for the given values n and r, both the matching energy ME(G) and the largest matching root λ1(G) of complete r-partite graphs are minimal for complete split graph CS(n,r-1) and are maximal for Turán graph T(n,r).

scholarly journals Uniquely Satisfiable d-Regular (k,s)-SAT Instances

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 569
Author(s):  
Zufeng Fu ◽  
Daoyun Xu
Keyword(s):  
Nonnegative Integer ◽  
Critical Function ◽  
Absolute Value ◽  
The Absolute ◽  
The Difference ◽  
The Given

Unique k-SAT is the promised version of k-SAT where the given formula has 0 or 1 solution and is proved to be as difficult as the general k-SAT. For any k ≥ 3 , s ≥ f ( k , d ) and ( s + d ) / 2 > k − 1 , a parsimonious reduction from k-CNF to d-regular (k,s)-CNF is given. Here regular (k,s)-CNF is a subclass of CNF, where each clause of the formula has exactly k distinct variables, and each variable occurs in exactly s clauses. A d-regular (k,s)-CNF formula is a regular (k,s)-CNF formula, in which the absolute value of the difference between positive and negative occurrences of every variable is at most a nonnegative integer d. We prove that for all k ≥ 3 , f ( k , d ) ≤ u ( k , d ) + 1 and f ( k , d + 1 ) ≤ u ( k , d ) . The critical function f ( k , d ) is the maximal value of s, such that every d-regular (k,s)-CNF formula is satisfiable. In this study, u ( k , d ) denotes the minimal value of s such that there exists a uniquely satisfiable d-regular (k,s)-CNF formula. We further show that for s ≥ f ( k , d ) + 1 and ( s + d ) / 2 > k − 1 , there exists a uniquely satisfiable d-regular ( k , s + 1 ) -CNF formula. Moreover, for k ≥ 7 , we have that u ( k , d ) ≤ f ( k , d ) + 1 .

STILLING BASIN WITH A FLOW SWIRLING

2021 ◽  
pp. 79-86
Author(s):  
A. P. GURJEV ◽  
◽  
M. M. CHUMICHEVA ◽  
O. V. МАREEVA ◽  
A. S. VERHOGLYADOVA ◽  
...  
Keyword(s):  
Uniform Distribution ◽  
Inlet Section ◽  
Output Section ◽  
Stilling Basin ◽  
Main Disadvantage ◽  
Diversion Channel ◽  
Stilling Basins ◽  
Applied Design ◽  
The Given ◽  
Made In

In the given materials there is given an analysis of the operation of existing constructions of devices for dissipation of excess energy of idle water discharges at hydraulic engineering facilities. The most applied design for dissipation of fl ow energy in the practice of hydraulic building in the world is stilling basins with straight axis made in prismatic or trapezoidal shapes which is appealing in their simplicity. The main disadvantage of these stilling wells in case of their using together with tubular spillways, especially having several strings, is practical impossibility to provide uniform distribution of specific discharges at the outlet from the spillway. This is connected with the fact that with several strings it is difficult to provide uniform distribution of specific discharges in the inlet section of the stilling well, it causes appearance of unstable regimes during operation of the stilling basin, especially in case of spillway operation with incomplete front which makes them inapplicable exactly for multi-point tubular spillways. At the same time, by deforming the stilling basin well flow in the form of a spiral, it is possible to reduce the length of the spilling basin by creating the possibility of the planned symmetric spreading of the flow in the output section in the diversion channel of the stilling basin, allowing using it if necessary to repeatedly expand the flow behind the spillway.

scholarly journals ALGORITHM FOR SOLVING THE INVERSE PROBLEMS OF ECONOMIC ANALYSIS IN THE PRESENCE OF LIMITATIONS

2020 ◽  
Vol 1 ◽  
pp. 70-78
Author(s):  
Ekaterina Gribanova
Keyword(s):  
Inverse Problem ◽  
Linear Programming ◽  
Inverse Problems ◽  
Iterative Procedure ◽  
Management Decision ◽  
Relative Importance ◽  
The Absolute ◽  
The Given ◽  
Number Of Iterations ◽  
Management Decision Support

The solution of inverse problems is considered taking into account the restrictions using inverse calculations. An algorithm is proposed for solving the inverse problem, taking into account restrictions while minimizing the sum of the absolute values of the changes in the arguments. The problem of determining the increments of the function arguments is presented as a linear programming problem. The algorithm includes solving the inverse problem with the help of inverse calculations while minimizing the sum of the absolute changes in the arguments, checking the correspondence of the obtained arguments to the given restrictions, adjusting the value of the argument if it goes beyond the limits of acceptable values, and changing the varied arguments to achieve the given value of the resulting indicator. The solution of two problems with the additive and mixed dependence between the arguments of the function is considered. It is shown that the solutions obtained in this case are consistent with the result of using an iterative procedure based on changing the resulting value to a small value until a given result is achieved, and the results are compared with solving problems using the MathCad mathematical package. The advantage of the algorithm is a smaller number of iterations compared to the known method, as well as the absence of the need to use coefficients of relative importance. The presented results can be used in management decision support systems

Smooth B-Spline Curves Extension with Ordered Points Constraint

2011 ◽  
Vol 311-313 ◽  
pp. 1439-1445 ◽  
Author(s):  
Jin Xu
Keyword(s):  
Experimental Results ◽  
Maximum Deviation ◽  
Curve Segment ◽  
B Spline ◽  
Original Curve ◽  
Spline Curves ◽  
Minimum Number ◽  
The Given ◽  
Curve Extension ◽  
Extension Process

An algorithm for extending B-spline curves with a sequence of ordered points constraint is presented based on the curve unclamping algorithm. The ordered points are divided into two categories: interpolation points and approximation points. The number of interpolation points increases gradually during the curve extension process. The most important feature of this algorithm is the ability to optimize the knots of the extended curve segment according to the ordered points. Thus, with minimum number of interpolation points, the maximum deviation of the extended curve segment from the ordered points is less than the given tolerance. The extended curve segment connects to the original curve with maximum continuity intrinsically. Several experimental results have shown the validity and applicability of the proposed algorithm.

scholarly journals Comparative Analyses of the Self-Sealing Mechanisms in Leaves of Delosperma cooperi and Delosperma ecklonis (Aizoaceae)

2020 ◽  
Vol 21 (16) ◽  
pp. 5768
Author(s):  
Linnea Hesse ◽  
Tim Kampowski ◽  
Jochen Leupold ◽  
Sandra Caliaro ◽  
Thomas Speck ◽  
...  
Keyword(s):  
South Africa ◽  
Leaf Morphology ◽  
The Self ◽  
Ecological Niches ◽  
Vascular Strand ◽  
Closely Related Species ◽  
Oceanic Climate ◽  
The Absolute ◽  
The Given ◽  
Semi Arid

Within the Aizoaceae, the genus Delosperma exhibits a vast diversification colonizing various ecological niches in South-Africa and showing evolutionary adaptations to dry habitats that might include rapid self-sealing. Leaves of Delosperma react to external damage by the bending or contraction of the entire leaf until wound edges are brought into contact. A study of leaf morphology and anatomy, biomechanics of entire leaves and individual tissues and self-sealing kinematics after a ring incision under low and high relative humidity (RH) was carried out comparing the closely related species Delosperma cooperi and Delosperma ecklonis, which are indigenous to semi-arid highlands and regions with an oceanic climate, respectively. For both species, the absolute contractions of the examined leaf segments (“apex”, “incision”, “base”) were more pronounced at low RH levels. Independent of the given RH level, the absolute contractions within the incision region of D. cooperi were significantly higher than in all other segments of this species and of D. ecklonis. The more pronounced contraction of D. cooperi leaves was linked mainly to the elastic properties of the central vascular strand, which is approximately twice as flexible as that of D. ecklonis leaves.

On Katětov Spaces

1989 ◽  
Vol 32 (4) ◽  
pp. 425-433 ◽  
Author(s):  
Jack Porter ◽  
Mohan Tikoo
Keyword(s):  
Recent Work ◽  
Closed Subspace ◽  
Closed Space ◽  
Closed Set ◽  
Scattered Space ◽  
The Absolute ◽  
The Given

AbstractRecent work by Krystock, Porter, and Vermeer has emphasized the importance of the concepts of Katětov spaces and H-sets in the theory of H-closed spaces. These properties are closely related to being the θ-closure of some set and being the adherence of an open filter. This relationship is developed by establishing, among other facts, that an H-closed space in which every closed set is the θ-closure of some set is compact and the θ-closure of a subset of an H-closed space is Katětov and characterizing the open filter adhérences of a space as precisely those sets which are the image of a closed set of the absolute of the space. Also, examples are given of a countable, scattered space which is not Katětov and an H-closed space with an H-closed subspace which is not the θ-closure of any subset of the given space.

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