On a problem concerning quaternion valued Gaussian random variables

2010 ◽  
Vol 17 (4) ◽  
pp. 629-634
Author(s):  
George Chelidze ◽  
Nicholas Vakhania
Keyword(s):  
Linear Form ◽  
Random Variables ◽  
Characterization Theorem ◽  
Random Variable ◽  
Negative Answer ◽  
The Other ◽  
Gaussian Random Variables ◽  
Gaussian Distributions ◽  
Left Hand ◽  
The Right

Abstract In the present paper we construct an example of a quaternion random variable such that Polya's type characterization theorem of Gaussian distributions does not hold. The matter is that in the linear form, consisting of the independent copies of quaternion random variables, a part of the quaternion coefficients is written on the right hand side and the other part on the left-hand side. This gives a negative answer to the question posed in [Vakhania and Chelidze, Teor. Veroyatnost. i Primenen. 54: 337–344, 2009].

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

scholarly journals On a characterization theorem on a-adic solenoids

2019 ◽  
Vol 489 (3) ◽  
pp. 227-231
Author(s):  
G. M. Feldman
Keyword(s):  
Gaussian Distribution ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
The Other ◽  
Independent Random Variables ◽  
Linear Forms ◽  
The Real

According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an -adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the -adic solenoid.

§ XI.—Hellenistic Mycenae

1923 ◽  
Vol 25 ◽  
pp. 408-428
Author(s):  
C. A. Boethius
Keyword(s):  
Common Type ◽  
The Other ◽  
The South ◽  
Left Hand ◽  
The Right

Among the ruins of the Hellenistic buildings at the south end of the Great Ramp, in the fourth or southern chamber (Pl. I. 34), three fragments of a stele (now in the Nauplia Museum) were found. The stele is of a simple and common type, and is made of the same white limestone as the other Mycenaean stele found by Tsountas, which it closely resembles even in its weathering. Except for the top left-hand corner and a gap on the right side the whole stele is preserved. It is ·969 m. in height, ·41–·436 m. in breadth (·41 m. at the ninth line of the inscription) and ·11–·125 m. thick. At the top there is a plain frieze, ·065 m. high : ·02 m. below the frieze begins an inscription which fills twenty lines and ends ·50 m. above the bottom of the stele. The letters are ·008–·01 m. high. The space between the lines is ·009–·011 m. The surface of the stone is very much worn, and it was consequently difficult to make out the letters and their accurate forms. The sketch (Fig. 93) shows the arrangement of the text.

scholarly journals Handedness results from complementary hemispheric dominance, not global hemispheric dominance: evidence from mechanically coupled bilateral movements

2018 ◽  
Vol 120 (2) ◽  
pp. 729-740 ◽  
Author(s):  
Elizabeth J. Woytowicz ◽  
Kelly P. Westlake ◽  
Jill Whitall ◽  
Robert L. Sainburg
Keyword(s):  
Motor Control ◽  
Dynamic Control ◽  
The Other ◽  
Hemispheric Dominance ◽  
Control Mechanisms ◽  
Left Hand ◽  
Right Hand ◽  
Other Hand ◽  
Task Component ◽  
The Right

Two contrasting views of handedness can be described as 1) complementary dominance, in which each hemisphere is specialized for different aspects of motor control, and 2) global dominance, in which the hemisphere contralateral to the dominant arm is specialized for all aspects of motor control. The present study sought to determine which motor lateralization hypothesis best predicts motor performance during common bilateral task of stabilizing an object (e.g., bread) with one hand while applying forces to the object (e.g., slicing) using the other hand. We designed an experimental equivalent of this task, performed in a virtual environment with the unseen arms supported by frictionless air-sleds. The hands were connected by a spring, and the task was to maintain the position of one hand while moving the other hand to a target. Thus the reaching hand was required to take account of the spring load to make smooth and accurate trajectories, while the stabilizer hand was required to impede the spring load to keep a constant position. Right-handed subjects performed two task sessions (right-hand reach and left-hand stabilize; left-hand reach and right-hand stabilize) with the order of the sessions counterbalanced between groups. Our results indicate a hand by task-component interaction such that the right hand showed straighter reaching performance whereas the left hand showed more stable holding performance. These findings provide support for the complementary dominance hypothesis and suggest that the specializations of each cerebral hemisphere for impedance and dynamic control mechanisms are expressed during bilateral interactive tasks. NEW & NOTEWORTHY We provide evidence for interlimb differences in bilateral coordination of reaching and stabilizing functions, demonstrating an advantage for the dominant and nondominant arms for distinct features of control. These results provide the first evidence for complementary specializations of each limb-hemisphere system for different aspects of control within the context of a complementary bilateral task.

Rediscovering Leon Theremin

Tempo ◽  
1991 ◽  
pp. 18-23 ◽  
Author(s):  
Stephen Montague
Keyword(s):  
Electromagnetic Field ◽  
The Other ◽  
Electronic Instrument ◽  
Left Hand ◽  
Vertical Antenna ◽  
Right Hand ◽  
Concert Halls ◽  
The Right

In the early 1920s and 30s a strange electronic instrument found its way from Russia into some of the more fashionable ballrooms, night clubs, and concert halls in Europe and America. This exotic new invention, called the ‘theremin’ or ‘thereminvox’, caused a considerable stir. Part of the interest was its unusual sound (like a musical saw mated with a light soprano), but its most dramatic feature was that the performer never actually touched the instrument. He or she simply waved graceful hands near the two antennae (one set vertically, the other looped horizontally) to coax out seamless, melifluous melodies. The proximity of the right hand to the vertical antenna changed the ultrasonic electromagnetic field, thus changing the pitch over about a six-octave range. The left hand (or sometimes a foot pedal) controlled the volume. By gently shaking the right hand at the antenna a vibrato could be achieved, giving performances a little more musical (not to mention choreographic) interest. Fashionable women dressed in long gowns seemed to be favourite photographic subjects of the period as performers, as well as the inventor himself, poised ‘playing the rods’ in full dress tails, arms outstretched like a great conductor–or perhaps sorcerer.

scholarly journals XIV.—Ancient Gold Ornaments: described by John Yonge Akerman, Esq. Secretary

Archaeologia ◽  
1853 ◽  
Vol 35 (1) ◽  
pp. 190-193
Author(s):  
John Yonge Akerman
Keyword(s):  
Light Chain ◽  
The Body ◽  
The Other ◽  
Asia Minor ◽  
Plate Viii ◽  
Left Hand ◽  
Small Loop ◽  
The Individual ◽  
The Right ◽  
Of Greece

With the exception of Figs. 1, 2, 3, the Gold Ornaments engraved in Plate VIII. have no reference whatever to each other. The first three were obtained by Viscount Strangford, Director of the Society, from a Greek priest at Milo, in the year 1820. Figs. 1 and 3 appear to have formed the ends of a light chain, and the other (fig. 2) to have been pendent by a small loop on the top of the head. The figure has unfortunately lost the feet and the left hand, but the other parts are perfect. The right hand is raised in an admonitory attitude. The forehead appears as if encircled with a wreath, while the body is crossed by what would seem to be intended for the tendril of a vine. The necklace was formerly in the collection of the late Mr. H. P. Borrell, of Smyrna, but I am informed by his brother, Mr. Maximilian Borrell, who now possesses it, that no record exists of its discovery, and that he cannot learn the name of the individual from whom it was purchased. It was well known that Mr. H. P. Borrell was in the habit of purchasing ancient coins, which were sent to him from all parts of Greece and Asia-Minor, and that many rare and unique specimens fell into his hands, of which he contributed descriptions in various volumes of the Numismatic Chronicle. The necklace may, therefore, have been included in one of these numerous consignments, and we can scarcely indulge the hope that the place of its discovery will ever be made known. As an example of ancient art, it may vie with the most elaborate and beautiful specimens of goldsmiths' work of any age or period. The details are wonderfully minute and delicate, even the backs of the button-like objects at the ends of the pendent cords being elaborately finished.

Failure to Sing the Left-Hand Part of the Score during Piano Performance: Loss of the Pitch and Stroop Vocalizations

1989 ◽  
Vol 6 (3) ◽  
pp. 299-314 ◽  
Author(s):  
Yves Guiard
Keyword(s):  
The Other ◽  
Vocal Response ◽  
Left Hand ◽  
Performance Loss ◽  
Clear Cut ◽  
Right Hand ◽  
Hand Part ◽  
Continuous Regime ◽  
And Performance ◽  
The Right

An experiment compared the ability of classical pianists to sing, during keyboard performance, the right- and the left-hand part of the score being played. Upon instructions requiring them to "sing" one or the other voice of the score, the subjects spontaneously chose to sing and name the notes simultaneously, in keeping with the French traditional way of reading music, thus producing a two- dimensional tonal and verbal vocal act in response to each visual stimulus. Singing the right-hand part of the music, whether in unison with or in place of the right hand, while concurrently playing the left-hand part was judged easy by all subjects, and performance, typically, was correct in all respects. The other task, consisting of singing the left-hand part of the music, was judged more difficult by all subjects, and performance, more often than not, was poor. Careful inspection of the many errors that were recorded in the latter task revealed a few clear-cut regularities. Failures were vocal, but not manual. More specifically, vocal failures took place on the tonal dimension of the vocal response, but not on its verbal dimension: The song, but not the naming of the notes, was prone to fail, with either a loss of the pitch, or a systematic trend toward singing unduly—albeit accurately—the notes of the right-hand part. A number of subjects were found to display this intriguing tonal/verbal dissociation—naming a note at a pitch corresponding to another note—in a continuous regime. It is emphasized that this phenomenon amounts to the spontaneous production of musical events that belong to the Stroop category.

On a New Type of Vibrating Lift

1980 ◽  
Vol 102 (2) ◽  
pp. 264-269
Author(s):  
J. Inoue ◽  
Y. Araki ◽  
S. Kubo
Keyword(s):  
The Self ◽  
The Other ◽  
Vertical Position ◽  
Horizontal Position ◽  
Linear Vibration ◽  
Left Hand ◽  
Asynchronous Motors ◽  
Rotational Vibration ◽  
New Type ◽  
The Right

This paper investigates in detail the new vibrating lift made by utilizing the principle of the self-synchronization of mechanical vibrators. In a general way products ride up inclined way of the spiral trough of a vibrating lift, propelled by forces generated by two unbalanced rotors connected by the gear and driven by a motor, which are mounted on top of the structure in a horizontal position. This machine is a new type of vibrating lift. The axes of two unbalanced rotors are nonparallel and each driven by two asynchronous motors. One motor is positioned on the right hand side and the other is situated on the left hand side of the structure in a vertical position. In spite of the absence of any connection between two rotors, they rotate at the same speed and have the definite phase angle between them as the result of the phenomena of the self-synchronization under a certain condition. This phenomenon is also called entrainment. Accordingly, by the linear vibration in the direction of the axis of the structure and rotational vibration about the axis of the structure by two unbalanced rotors, products ride up inclined way of the spiral trough.

scholarly journals Synchronization Error of Drum Kit Playing with a Metronome at Different Tempi by Professional Drummers

2011 ◽  
Vol 28 (5) ◽  
pp. 491-503 ◽  
Author(s):  
Shinya Fujii ◽  
Masaya Hirashima ◽  
Kazutoshi Kudo ◽  
Tatsuyuki Ohtsuki ◽  
Yoshihiko Nakamura ◽  
...  
Keyword(s):  
Time Series ◽  
The Other ◽  
Synchronization Error ◽  
Left Hand ◽  
Snare Drum ◽  
Right Hand ◽  
The Absolute ◽  
The Right

the present study examined the synchronization error (SE) of drum kit playing by professional drummers with an auditory metronome, focusing on the effects of motor effectors and tempi. Fifteen professional drummers attempted to synchronize a basic drumming pattern with a metronome as precisely as possible at tempi of 60, 120, and 200 beats per minute (bpm). In the 60 and 120 bpm conditions, the right hand (high-hat cymbals) showed small mean SE (∼2 ms), whereas the left hand (snare drum) and right foot (bass drum) preceded the metronome by about 10 ms. In the 200 bpm condition, the right hand was delayed by about 10 ms relative to the metronome, whereas the left hand and right foot showed small SE (∼1 ms). The absolute values of SE were smaller than those reported in previous tapping studies. In addition, the time series of SE were significantly correlated across the motor effectors, suggesting that each limb synchronized in relation to the other limbs rather than independently with the metronome.

Greek Vases in the Otago Museum

1936 ◽  
Vol 56 (2) ◽  
pp. 235-236
Author(s):  
A. D. Trendall
Keyword(s):  
New Zealand ◽  
Fifth Century ◽  
The Other ◽  
Left Hand ◽  
Right Hand ◽  
Greek Vases ◽  
The Right

Of the recent acquisitions to the Classical Collection of the Otago Museum (Dunedin, New Zealand) the most noteworthy is a particularly fine Attic white ground lekythos of about the middle of the fifth century (Plate XIV). It stands 38 cm. high and is in an excellent state of preservation, having been most carefully repaired with a minimum of repainting, which has affected only the breast of the woman, the right hand of the warrior, and some details of the small figure on top of the stele.The design represents a stele scene of the sort so popular with lekythos artists of this period. To the left stands a woman wearing a sleeved chiton, so thin that it clearly allows her bowed legs to be seen through it; with her left hand she points downward to the base of the stele, which is adorned with a fillet and a wreath. On the other side stands a hoplite with his shield and spear;

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