scholarly journals Total Differentiability and Monogenicity for Functions in Algebras of Order 4

2021 ◽  
Vol 15 (2) ◽  
Author(s):  
I. Sabadini ◽  
D. C. Struppa
Keyword(s):  
Analytic Functions ◽  
Associative Algebras ◽  
Basic Tool ◽  
Algebraic Analysis ◽  
Italian School ◽  
Relevant Role

AbstractIn this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

On Some Relations Between Partial and Ordinary Differential Equations

1958 ◽  
Vol 10 ◽  
pp. 183-190 ◽  
Author(s):  
Erwin Kreyszig
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Complex Variable ◽  
Analytic Functions ◽  
Integral Operators ◽  
Basic Tool ◽  
Partial Differential ◽  
Image Position

The theory of solutions of partial differential equations (1.1) with analytic coefficients can be based upon the theory of analytic functions of a complex variable; the basic tool in this approach is integral operators which map the set of solutions of (1.1) onto the algebra of analytic functions. For certain classes of operators this mapping which is first defined in the small, can be continued to the large, cf. Bergman (3).

Glass Knife Geometry as Seen by the SEM

1971 ◽  
Vol 29 ◽  
pp. 454-455
Author(s):  
J. Temple Black
Keyword(s):  
Low Cost ◽  
Amorphous Material ◽  
Stress Concentrations ◽  
Basic Tool ◽  
Tool Materials ◽  
Optical Inspection ◽  
Surface Flaws ◽  
Slip Planes ◽  
Glass Knife ◽  
Diamond Knife

In ultramicrotomy, the two basic tool materials are glass and diamond. Glass because of its low cost and ease of manufacture of the knife itself is still widely used despite the superiority of diamond knives in many applications. Both kinds of knives produce plastic deformation in the microtomed section due to the nature of the cutting process and microscopic chips in the edge of the knife. Because glass has no well defined slip planes in its structure (it's an amorphous material), it is very strong and essentially never fails in compression. However, surface flaws produce stress concentrations which reduce the strength of glass to 10,000 to 20,000 psi from its theoretical or flaw free values of 1 to 2 million psi. While the microchips in the edge of the glass or diamond knife are generally too small to be observed in the SEM, the second common type of defect can be identified. This is the striations (also termed the check marks or feathers) which are always present over the entire edge of a glass knife regardless of whether or not they are visable under optical inspection. These steps in the cutting edge can be observed in the SEM by proper preparation of carefully broken knives and orientation of the knife, with respect to the scanning beam.

Hearing in Mice via GSR Audiometry

1963 ◽  
Vol 6 (4) ◽  
pp. 359-368 ◽  
Author(s):  
Charles I. Berlin
Keyword(s):  
Inverse Relationship ◽  
Sound Pressure ◽  
Single Units ◽  
Sensitivity Curve ◽  
Basic Tool ◽  
Eighth Nerve ◽  
Pure Tones ◽  
Conditioned Responses ◽  
Frequency Intensity ◽  
Near Threshold

Hearing in mice has been difficult to measure behaviorally. With GSR as the basic tool, the sensitivity curve to pure tones in mice has been successfully outlined. The most sensitive frequency-intensity combination was 15 000 cps at 0-5 dB re: 0.0002 dyne/cm 2 , with responses noted from 1 000 to beyond 70 000 cps. Some problems of reliability of conditioning were encountered, as well as findings concerning the inverse relationship between the size of GSR to unattenuated tones and the sound pressure necessary to elicit conditioned responses at or near threshold. These data agree well with the sensitivity of single units of the eighth nerve of the mouse.

Effect of Heart Rate Variability on Defensive Reaction and Eating Disorder Symptomatology in Chocolate Cravers

2009 ◽  
Vol 23 (3) ◽  
pp. 95-103 ◽  
Author(s):  
Sonia Rodríguez-Ruiz ◽  
Elisabeth Ruiz-Padial ◽  
Nieves Vera ◽  
Carmen Fernández ◽  
Lourdes Anllo-Vento ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Eating Disorder ◽  
Eating Behavior ◽  
Rest Period ◽  
Food Craving ◽  
Defensive Reaction ◽  
Relevant Role ◽  
Eating Disorder Symptomatology ◽  
Uncontrolled Eating

The study examines the effect of heart rate variability (HRV) on the cardiac defence response (CDR) and eating disorder symptomatology in chocolate cravers. Female chocolate cravers (n = 36) and noncravers (n = 36) underwent a psychophysiological test to assess their HRV during a 5-min rest period, followed by three trials to explore the CDR, elicited by an intense white noise, during the viewing of chocolate, neutral, and unpleasant pictures. After the test, participants completed a questionnaire to measure eating disorder symptomatology. The HRV was inversely related to the magnitude of the CDR and to eating disorder symptomatology in chocolate cravers. In addition, the HRV was inversely related to the magnitude of the CDR when viewing unpleasant pictures but not to neutral or chocolate ones, across all participants. These findings support the idea that poor autonomic regulation, indexed by low HRV, plays a relevant role in food craving and uncontrolled eating behavior.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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