scholarly journals On a Flat Triangular Form Based on the Extended Chained Form

2021 ◽  
Vol 54 (9) ◽  
pp. 245-252
Author(s):  
Conrad Gstöttner ◽  
Bernd Kolar ◽  
Markus Schöberl
Keyword(s):  
Triangular Form

Fault Tolerant Guidance of Under-Actuated Satellite Formation Flying Using Inter-Vehicle Coulomb Force

2019 ◽  
Vol 2 (1) ◽  
pp. 43-52
Author(s):  
Alireza Alikhani ◽  
Safa Dehghan M ◽  
Iman Shafieenejad
Keyword(s):  
Fault Tolerance ◽  
Formation Flying ◽  
Fault Tolerant ◽  
Coulomb Force ◽  
Control Law ◽  
Triangular Form ◽  
Satellite Formation Flying ◽  
Satellite Formation ◽  
Guidance Law ◽  
Tolerance Approach

In this study, satellite formation flying guidance in the presence of under actuation using inter-vehicle Coulomb force is investigated. The Coulomb forces are used to stabilize the formation flying mission. For this purpose, the charge of satellites is determined to create appropriate attraction and repulsion and also, to maintain the distance between satellites. Static Coulomb formation of satellites equations including three satellites in triangular form was developed. Furthermore, the charge value of the Coulomb propulsion system required for such formation was obtained. Considering Under actuation of one of the formation satellites, the fault-tolerance approach is proposed for achieving mission goals. Following this approach, in the first step fault-tolerant guidance law is designed. Accordingly, the obtained results show stationary formation. In the next step, tomaintain the formation shape and dimension, a fault-tolerant control law is designed.

scholarly journals The flame spectrum of carbon monoxide

1940 ◽  
Vol 176 (967) ◽  
pp. 505-521 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Carbon Monoxide ◽  
Electronic State ◽  
Excited Electronic State ◽  
Combustion Process ◽  
Wave Number ◽  
Band Spectrum ◽  
Liquid Form ◽  
Triangular Form ◽  
Reduced Pressure

The spectrum of the flame of carbon monoxide burning in air and in oxygen at reduced pressure has been photographed on plates of high contrast which display the band spectrum clearly above the continuous background. Greater detail has been obtained than has been recorded previously and new measurements are given. The structure of the spectrum has been studied systematically. It is shown that the bands occur in pairs with a separation of about 60 cm. -1 , this separation being due probably to the rotational structure. Various wave-number differences are found to occur frequently, and many of the strong bands are arranged in arrays using intervals of 565 and 2065 cm. -1 . The possible origin of the spectrum is discussed. The choice of emitter is limited to a polyatomic oxide of carbon, of which carbon dioxide is the most likely. The spectrum of the suboxide C 3 O 2 shows some resemblance to the flame bands, but this molecule is improbable as the emitter on other grounds. A peroxide C0 3 is also a possibility, but no evidence for the presence of this has been obtained from experiments on the slow combustion of carbon monoxide. Carbon dioxide in gaseous or liquid form is transparent through the visible and quartz ultra-violet, and the flame bands are not obtained from CO 2 in discharge tubes. Comparison with the Schumann-Runge bands of oxygen shows that it is possible that the flame bands may form part of the absorption band system of CO 2 which is known to exist below 1700 A if there is a big change in shape or size of the molecule in the two electronic states. The electronic energy levels of CO 2 are discussed. Since normal CO 2 is not built up from normal CO and oxygen, an electronic rearrangement of the CO 2 must occur after the combustion process. Mulliken has suggested that the molecule in the first excited electronic state, corresponding to absorption below 1700 A, may have a triangular form. The frequencies obtained from the flame bands are compared with the infra-red frequencies of CO 2 . The 565 interval may be identified with the transverse vibration v 2 , indicating that the excited electronic state is probably triangular in shape. The 2065 interval cannot, however, be identified with the asymmetric vibration v 3 with any certainty. If the excited electronic state of CO 2 is triangular, then molecules formed during the combustion by transitions from this level to the ground state may be “vibrationally activated”. This is probably the reason for many of the peculiarities of the combustion of carbon monoxide.

A Markovian Finishing Process

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. A. S. Mohamed
Keyword(s):  
Triangular Form ◽  
Workpiece Surface ◽  
Finishing Process ◽  
Tool Surface ◽  
Markov Matrix ◽  
Abrasive Surface ◽  
Matrix Mapping ◽  
Abrasive Tools ◽  
Finishing Processes ◽  
Abrasive Paper

Addressed is the mechanism of finishing processes for a workpiece surface using hard abrasive tools such as grinding, abrasive paper, and filing. The mechanism is intended to monitor the gradual changes of the workpiece surface state roughness as the tool is applied for several strokes. Based on a number of common features, the present study simulates each rubbing stroke as a Markov process, and each set of several strokes as a Markov chain. In the simulating model, the discrete probabilistic properties of a specific tool abrasive surface can be expressed in terms of a corresponding Markov matrix operator. Thus, the tool action after one rubbing stroke is obtained via a matrix mapping from a given state roughness to a subsequent state roughness of the workpiece surface. Although the suggested model is capable to handle a comprehensive finishing mechanism, the study focuses on the simple case of zero feeding using a hard abrasive tool, in which the Markov matrix shrinks to a special triangular form. Main findings show that major aspects of the tool surface are transferred to the stepwise roughness state of the workpiece immediately after the first stroke. In addition, regardless of the initial roughness state of the workpiece surface, whether with flat or randomly distributed heights, the ultimate state roughness is unique and definitely features the theoretical case of a plain flat surface. However, this theoretical case is infeasible since it can only be reached after infinite number of strokes.

scholarly journals The influence of the charge shape on heat exchange of a recessed nozzle

2021 ◽  
Vol 2057 (1) ◽  
pp. 012013
Author(s):  
B Ya Benderskiy ◽  
A A Chernova
Keyword(s):  
Heat Exchange ◽  
Power Plant ◽  
Combustion Products ◽  
Triangular Form ◽  
Topological Features ◽  
Exchange Processes ◽  
Charge Shape ◽  
Intensification Of Heat Exchange ◽  
Thermally Conductive ◽  
Control Volumes

Abstract The paper deals with the numerical simulation of the flow of thermally conductive viscous gaseous combustion products in the flow paths of a power plant. The influence of the shape of the mass supply surface on the gas dynamics and heat exchange near the recessed nozzle of the power plant is investigated. The coupled problem of heat exchange is solved by the method of control volumes. It is shown that the compensator geometry determines the localization of both the topological features of the flow near the recessed nozzle and the position of local maximums of the heat transfer coefficient. It has been revealed that The use of a channel with a star-shaped cross section and a triangular form of compensator rays leads to an intensification of heat exchange processes near a recessed nozzle.

Reduction of a Square Matrix to Triangular Form

1980 ◽  
Vol 64 (430) ◽  
pp. 266
Author(s):  
F. Gerrish
Keyword(s):  
Triangular Form ◽  
Square Matrix

Studies in Canarium urceus (Linné, 1758) Part 2: Strombus anatellus Duclos, 1844, Strombus crassilabrum Anton, 1839, Strombus incisus Wood, 1828 and Strombus ustulatus form laevis Dodge, 1946 (Neostromboidae: Strombidae)

The Festivus ◽  
2020 ◽  
Vol 52 (4) ◽  
pp. 335-344
Author(s):  
Stephen Maxwell ◽  
Tasmin Rymer ◽  
Bradley Congdon ◽  
Aart Dekkers
Keyword(s):  
New Taxa ◽  
The Philippines ◽  
Type Material ◽  
Valid Species ◽  
Triangular Form ◽  
Nomen Dubium ◽  
Written Descriptions

Many valid species can hide buried within prior taxonomic revisions. These need to be examined before the taxonomist embarks on the challenging task of naming new taxa. In this study we re-examine the synonyms complied by Abbott (1960) under Canarium urceus (Linné, 1758), examining each taxon for morphological clarity and distinctiveness. After considering the written descriptions and type material in light of prior revisions, we suggest that there are three valid species buried within the C. urceus synonymy of Abbott. All three species can be differentiated from C. urceus in general form, being less equi-triangulate and lacking the strong shoulder knobbing of that species. In addition, all three species are distinguishable by their distinctive aperture colouration. Canarium urceus possesses a typically black aperture, Canarium anatellum (Duclos, 1844) can be differentiated by its typically uniformly red/orange aperture, while Canarium incisum (Wood, 1828)is recognisable by the typically orange columella and outer lip, and a more triangular form. Strombus ustulatus form laevis Dodge, 1946 is the classical well-known form from the Philippines and elsewhere that is recognisable by its white columella. As the name laevis was preoccupied, we have renamed the species Canarium esculentum nomen novem. We assessed Strombus crassilabrum Anton, 1839 to be a nomen dubium. Further, our revision provides an improved hypothetical framework for the evolution and radiation of this most adaptable and variable of organisms, through increased clarity, and the re-circumscription of hitherto described taxa with distinctive morphotypes and separate biogeographical ranges.

Unitary Transformations

1954 ◽  
Vol 6 ◽  
pp. 69-72 ◽  
Author(s):  
B. E. Mitchell
Keyword(s):  
Canonical Form ◽  
Unitary Transformation ◽  
General Pattern ◽  
Jordan Form ◽  
Unitary Matrix ◽  
Complex Matrices ◽  
Triangular Form ◽  
Unitary Transformations

We consider the problem of finding a unique canonical form for complex matrices under unitary transformation, the analogue of the Jordan form (1, p. 305, §3), and of determining the transforming unitary matrix (1, p. 298, 1. 2). The term “canonical form” appears in the literature with different meanings. It might mean merely a general pattern as a triangular form (the Jacobi canonical form (8, p. 64)). Again it might mean a certain matrix which can be obtained from a given matrix only by following a specific set of instructions (1). More generally, and this is the sense in which we take it, it might mean a form that can actually be described, which is independent of the method used to obtain it, and with the property that any two matrices in this form which are unitarily equivalent are identical.

Observer-Based Control of Nonlinear Time-Delay Systems in Lower-Triangular Form

2009 ◽  
Author(s):  
Salim Ibrir
Keyword(s):  
Time Delay ◽  
Small Time ◽  
Nonlinear Observer ◽  
Delay Systems ◽  
Linear Feedback ◽  
Time Delay Systems ◽  
Triangular Form ◽  
Small Time Delay ◽  
System Nonlinearity ◽  
Delay Dependent

Time-delay systems is a special class of dynamical systems that are frequently present in many fields of engineering. It has been shown in the literature that the existence of a stabilizing observer-based controller is related to delay-dependent conditions that are generally satisfied for a small time delay. Motivating works towards reducing the conservatism of the results are among the on-going research topics especially when partial-state measurements are imposed. This paper investigates the problem of observer-based stabilization of a class of time-delay nonlinear systems written in triangular form. First, we show that a delay nonlinear observer is globally convergent under the global Lipschitz condition of the system nonlinearity. Then, it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay. Illustrative example is provided to approve the theoretical results.

scholarly journals Some Theorems On Matrices With Real Quaternion Elements

1955 ◽  
Vol 7 ◽  
pp. 191-201 ◽  
Author(s):  
N. A. Wiegmann
Keyword(s):  
Similarity Transformation ◽  
Elementary Divisor ◽  
Quaternion Matrix ◽  
Unitary Similarity ◽  
Triangular Form ◽  
Quaternion Matrices ◽  
Divisor Theory ◽  
Real Quaternion ◽  
Unitary Similarity Transformation

Matrices with real quaternion elements have been dealt with in earlier papers by Wolf (10) and Lee (4). In the former, an elementary divisor theory was developed for such matrices by using an isomorphism between n×n real quaternion matrices and 2n×2n matrices with complex elements. In the latter, further results were obtained (including, mainly, the transforming of a quaternion matrix into a triangular form under a unitary similarity transformation) by using a different isomorphism.

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