scholarly journals Calculation of vectorial derivatives for functions of a quaternion variable and their properties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ji Eun Kim
Keyword(s):  
Elementary Functions ◽  
Left And Right ◽  
The Difference ◽  
Derivatives Of ◽  
Vector Part ◽  
Made In

AbstractVarious attempts have been made in defining the derivative of a quaternionic function due to the noncommutativity of the product over quaternions. We observe that the difference in the left and right operations caused by the noncommutativity of the quaternion product is determined by the vector part of the quaternion. In this paper, we propose a corresponding derivative to replace the derivative of a quaternion-valued function of a quaternionic variable using the component terms of a quaternion. Further, the analogous constant, product, and quotient rules for the proposed calculations are given. Application of the proposed derivatives is provided to compute the derivatives of elementary functions. Several illustrations are also presented.

Energy Approximation

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Main Lemma ◽  
The Other ◽  
Coarse Scale ◽  
Continuous Solutions ◽  
Material Derivative ◽  
Energy Variation ◽  
Energy Approximation ◽  
The Difference ◽  
Derivatives Of

This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.

Effects of avertin versus xylazine-ketamine anesthesia on cardiac function in normal mice

2001 ◽  
Vol 281 (5) ◽  
pp. H1938-H1945 ◽  
Author(s):  
Chari Y. T. Hart ◽  
John C. Burnett ◽  
Margaret M. Redfield
Keyword(s):  
Cardiac Function ◽  
Diastolic Pressure ◽  
Systolic Function ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Lv Function ◽  
Ketamine Anesthesia ◽  
The Difference ◽  
And Function ◽  
Derivatives Of

Anesthetic regimens commonly administered during studies that assess cardiac structure and function in mice are xylazine-ketamine (XK) and avertin (AV). While it is known that XK anesthesia produces more bradycardia in the mouse, the effects of XK and AV on cardiac function have not been compared. We anesthetized normal adult male Swiss Webster mice with XK or AV. Transthoracic echocardiography and closed-chest cardiac catheterization were performed to assess heart rate (HR), left ventricular (LV) dimensions at end diastole and end systole (LVDd and LVDs, respectively), fractional shortening (FS), LV end-diastolic pressure (LVEDP), the time constant of isovolumic relaxation (τ), and the first derivatives of LV pressure rise and fall (dP/d t max and dP/d t min, respectively). During echocardiography, HR was lower in XK than AV mice (250 ± 14 beats/min in XK vs. 453 ± 24 beats/min in AV, P < 0.05). Preload was increased in XK mice (LVDd: 4.1 ± 0.08 mm in XK vs. 3.8 ± 0.09 mm in AV, P < 0.05). FS, a load-dependent index of systolic function, was increased in XK mice (45 ± 1.2% in XK vs. 40 ± 0.8% in AV, P < 0.05). At LV catheterization, the difference in HR with AV (453 ± 24 beats/min) and XK (342 ± 30 beats/min, P < 0.05) anesthesia was more variable, and no significant differences in systolic or diastolic function were seen in the group as a whole. However, in XK mice with HR <300 beats/min, LVEDP was increased (28 ± 5 vs. 6.2 ± 2 mmHg in mice with HR >300 beats/min, P < 0.05), whereas systolic (LV dP/d t max: 4,402 ± 798 vs. 8,250 ± 415 mmHg/s in mice with HR >300 beats/min, P < 0.05) and diastolic (τ: 23 ± 2 vs. 14 ± 1 ms in mice with HR >300 beats/min, P < 0.05) function were impaired. Compared with AV, XK produces profound bradycardia with effects on loading conditions and ventricular function. The disparate findings at echocardiography and LV catheterization underscore the importance of comprehensive assessment of LV function in the mouse.

scholarly journals XIX. On the difference of meridians of the Royal Observatories of Greenwich and Paris

1827 ◽  
Vol 117 ◽  
pp. 286-296 ◽  
Keyword(s):  
The Other ◽  
Detailed Account ◽  
Sidereal Time ◽  
Methods Of Calculation ◽  
Royal Observatory ◽  
The Difference ◽  
Made In

In the Philosophical Transactions for 1826, Part II. Mr. Herschel has given a detailed account of observations, which were made in the month of July, 1825, for the purpose of ascertaining the difference of the meridians of the Royal Observatories of Greenwich and Paris, with a computation of these observations, from which the most probable value of the difference of longitude appears to be 9 m 21 s. 6. But I have perceived that in the copy of the observations delivered to him from the Royal Observatory of Greenwich, an error of one second has been committed; as the true sidereal time of the observation made there on 21st July, ought to be 17 h 38 m 57·12 in place of 17 h 38 m 56 s. 10, set down in the Table p. 104, which he informs me was computed at the Observatory, and officially communicated to him from the Astronomer Royal. This error seems to have had its origin in the little Table at the bottom of page 103; for, on subtracting the error of the clock, 47 s. 37, from the time 18 h 8 m 30 s. 40, the true sidereal time is 18 h 7 m 43 s. 03, instead of 18 h 7 m 42 s. 03, there given. The error in the result of that day’s observations, arising from this cause, has been partly compensated by a mistake of three tenths of a second, which has occurred in calculating the combined observations of the same day, the gain of mean on sidereal time being stated to be — 4 s. 54 (pp. 120 and 122), in place of — 4 s. 24. On checking the other observations, a few trifling alterations appear to be necessary upon the Greenwich Table of sidereal time, from the data given along with it. These seem to be occasioned by different methods of calculation, and indeed are hardly worthy of notice. The French astronomers not having given the data on which the calculations of the sidereal times at Paris are founded, they are assumed to be correct.

Study of the Characteristics of the Pulmonary Vein and Superior Vena Cava of Rabbits

2021 ◽  
Vol 11 (1) ◽  
pp. 112-122
Author(s):  
Pan Wang ◽  
Xin-Chun Yang ◽  
Xiu-Lan Liu ◽  
Rong-Feng Bao ◽  
Huai-Yu Ding ◽  
...  
Keyword(s):  
Action Potential ◽  
Pulmonary Vein ◽  
Refractory Period ◽  
Potassium Current ◽  
Superior Vena ◽  
Vena Cava ◽  
Current Intensity ◽  
Left And Right ◽  
The Difference ◽  
Right Atria

Background: This study aims to (1) investigate the characteristics of the action potential and triggering activity of cardiomyocytes in the pulmonary vein (PV) and superior vena cava (SVC) of rabbits and (2) study the features of cation currents in cardiomyocytes in rabbit PV and SVC-inward rectifier potassium current (IK1), transient outward potassium current (Ito), and non-selective cation currents (INSCC). Methods: The standard glass microelectrode and whole-cell patch-clamp techniques were used to record the action potential and various currents in the above cells. Results: (1) Cardiomyocytes in either PV or SVC had longer action potential durations than in the adjacent atrium, and spontaneous early after depolarization (EAD) could occur in both PV and SVC under normal physiological conditions. (2) The action potential in PV cardiomyocytes had a relative refractory period but did not have an absolute refractory period, and this characteristic enabled a premature beat that triggered a second plateau response, which led to EAD. (3) INSCC was found for the first time in the PV, SVC, and atria. (4) The current intensity of IK1, Ito, and INSCC was significantly lower in the PV and SVC than in the left and right atria, and the difference in the current intensity in INSCC could influence the action potential. Conclusions: PV and SVC can both initiate and maintain AF, but PV is the primary ectopic foci in initiating AF. The present study found that the second plateau response was easily induced in cardiomyocytes in PA shortly after depolarization. This was a specific characteristic of the action potential of PV. In addition, we preliminarily analyzed the differences in the main outward currents and noted a voltage-dependent INSCC in both PV and SVC rabbits’ cardiomyocytes. Furthermore, the current intensities of IK1, Ito, and INSCC were significantly lower in the PV and SVC than in the left and right atria, and the difference in the current intensity of INSCC influenced the action potential. The different permeability of INSCC for cations at different phases may play a role in inducing EAD.

Neural network processing of radar scanning data array

2021 ◽  
Author(s):  
V.E. Dmitriyev ◽  
D.V. Popov ◽  
V.A. Shakhnov
Keyword(s):  
Spatial Perception ◽  
Digital Processing ◽  
Radar Data ◽  
Information Value ◽  
Data Array ◽  
Additional Information ◽  
Distribution Of Values ◽  
The Difference ◽  
Radar Data Processing ◽  
Made In

This article deals with the digital processing of a matrix radar image. The information received from the radar scanner needs to be transformed to enable visual perception. The article describes the main methods of digital processing of matrix data, presents the images transformed by them. The aim of the article was the development of a radar data processing algorithm that identifies the contours and edges of examined objects. The authors propose an algorithm for isolating the geometric structure of the scanned area. The difference between the processing method and the known analogues is based on the nature of the change in the values of the array being processed and consists in the double operation of extracting the gradient of the distribution of values. The software implementation of the algorithm is made in C++ using methods from an open library of computer vision. The efficiency of the algorithm was estimated based on comparison with the algorithms for determining edges based on linear filtering and neural networks. The results of the work can be used to create software for mobile short-range radar devices. Imaging from object boundaries and their edges provides spatial perception of the image by the operator, and free areas are available for rendering additional information. This solution allows you to combine scanning devices and thereby increase the information value of the result.

Kinetic parameters of hexose transport in hybrids between malignant and nonmalignant cells

1983 ◽  
Vol 62 (1) ◽  
pp. 49-80
Author(s):  
M.K. White ◽  
M.E. Bramwell ◽  
H. Harris
Keyword(s):  
Kinetic Parameters ◽  
Malignant Cell ◽  
Hexose Transport ◽  
Hybrid Cells ◽  
Michaelis Constant ◽  
Independent Measurement ◽  
The Difference ◽  
Hexose Uptake ◽  
Derivatives Of

Matched pairs of isogeneic hybrid cells, in which one member of the pair was malignant and the other not, were used to examine the linkage between malignancy and functional alterations in hexose transport. The kinetic parameters of uptake of 2-deoxy-D-glucose were measured in a range of such hybrids, both human and murine. Some other malignant cell lines were also examined and were compared with non-tumorigenic derivatives of tumour cells selected by exposure to the lectin, wheat-germ agglutinin. In every case, malignancy, as defined by the ability of cells to grow progressively in vivo, was found to be linked to a decrease in the Michaelis constant of hexose uptake. Independent measurement of the transport and phosphorylation reactions involved in hexose uptake revealed that this decrease was determined by the membrane transport system. The difference in Michaelis constant between malignant and non-malignant cells was observed with 3-O-methylglucose, a hexose that is transported into the cell but not further metabolized. The activity of hexokinase in cell homogenates was higher than the level that would be required to cope with transport and showed no correlation with tumorigenicity. Measurement of the uptake of D-glucose itself, by a rapid filtration centrifugation method, gave results similar to those obtained with 2-deoxy-D-glucose.

Localizing cross-linguistic variation in Tense systems: On telicity and stativity in Swedish and English

2012 ◽  
Vol 35 (1) ◽  
pp. 27-70
Author(s):  
Björn Lundquist
Keyword(s):  
Romance Languages ◽  
Linguistic Variation ◽  
Verb Morphology ◽  
Reference Time ◽  
Lexical Aspect ◽  
Temporal Interpretation ◽  
Viewpoint Aspect ◽  
The Difference ◽  
Made In

It is well known that the aktionsart/lexical aspect of a predicate influences the temporal interpretation and the aspectual marking of a sentence, and also that languages differ with respect to which aktionsart properties feed into the tense-aspect system (see e.g. Bohnemeyer & Swift 2004). In this paper, I try to pin down the exact locus of variation between languages where the stative–dynamic distinction is mainly grammaticized (e.g. English, Saamáka) and languages where the telic–atelic distinction is mainly grammaticized (e.g. Swedish, Chinese and Russian). The focus will be on the differences between English and Swedish, and I will argue that these two languages crucially differ in the nature of Assertion Time (or Topic/Reference Time, Klein 1994, Demirdache & Uribe-Etxebarria 2000): whereas the assertion time in English is always punctual in imperfective contexts, assertion time in Swedish can extend to include minimal stages of events. The Assertion Time is introduced by a (viewpoint) aspect head that is present in both languages, but not phonologically realized. The difference can thus not be ascribed to the presence or absence of overt tense, aspect or verb morphology, or to a special tense value, as argued in one way or other by, for example, Giorgi & Pianesi (1997), Demirdache & Uribe-Etxebarria (2000) and Ramchand (2012). Once this factor (i.e. the nature of Assertion Time) has been isolated, it becomes evident that all verbs in English and Swedish, regardless of telicity or dynamicity, can be assigned either a perfective or an imperfective value. Moreover, I will argue that the English progressive–non-progressive (or ‘simple’) distinction is independent of viewpoint aspect (i.e. the perfective– imperfective distinction) made in, for example, the Romance languages.

scholarly journals XXXIV. Observations on the transit of Ve­nus, June the 6th, 1761, made in Spital-Square; the longitude of which is 4' 11" west of the Royal Observatory at Green­wich, and the latitude 51° 31' 15" north

1761 ◽  
Vol 52 ◽  
pp. 182-183
Keyword(s):  
The Sun ◽  
Royal Observatory ◽  
The Mean ◽  
The Difference ◽  
Made In

Having measured the diameter of Venus, on the sun, three times, with the object-glass micrometer, the mean was found to be 58 seconds; and but 6/10 of a second, the difference of the extremes.

Errors in Estimating the Orientation of Dot Patterns

Perception ◽  
1989 ◽  
Vol 18 (2) ◽  
pp. 237-242 ◽  
Author(s):  
P Lánský ◽  
Naum Yakimoff ◽  
T Radil ◽  
L Mitrani
Keyword(s):  
Pattern Analysis ◽  
Frontoparallel Plane ◽  
The Subject ◽  
Left And Right ◽  
The Mean ◽  
The Difference

The error in estimating the orientation of a dot pattern was measured as the difference between the orientation of the least-squared-distances line (LS-line) of the pattern and the orientation of a line adjusted by the subject to match the perceived orientation of the pattern. Analysis of the mean errors (averaged over ten subjects) obtained for one hundred patterns confirmed that the orientation of the LS-line represents the orientation of elongated dot-patterns. It is shown that estimated orientation was systematically biased towards the nearest 45° oblique meridian. This bias points to the importance of the ±45° directions as natural norms for left- and right-side tilt in the frontoparallel plane.

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