Cycloidal algebras

AbstractIn this paper we introduce for an arbitrary algebra (groupoid, binary system) (X; *) a sequence of algebras (X; *)n = (X; ∘), where x ∘ y = [x * y]n = x * [x * y]n−1, [x * y]0 = y. For several classes of examples we study the cycloidal index (m, n) of (X; *), where (X; *)m = (X; *)n for m > n and m is minimal with this property. We show that (X; *) satisfies the left cancellation law, then if (X; *)m = (X; *)n, then also (X; *)m−n = (X; *)0, the right zero semigroup. Finite algebras are shown to have cycloidal indices (as expected). B-algebras are considered in greater detail. For commutative rings R with identity, x * y = ax + by + c, a, b, c ∈ ℝ defines a linear product and for such linear products the commutativity condition [x * y]n = [y * x]n is observed to be related to the golden section, the classical one obtained for ℝ, the real numbers, n = 2 and a = 1 as the coefficient b.

Download Full-text

EVERYDAY PRACTICE OF MOTHERS IN A PROVINCIAL SOVIET CITY IN THE 1950–60S

Bulletin of the Kostroma state University ◽

10.34216/1998-0817-2020-26-2-42-51 ◽

2020 ◽

pp. 42-51

Author(s):

Irina V. Bogdashina

Keyword(s):

Well Being ◽

Reproductive Behaviour ◽

Working Mother ◽

Material Wealth ◽

The Real ◽

Raising Children ◽

Diffi Cult ◽

The Family ◽

The Right

The article reveals the measures undertaken by the Soviet state during the “thaw” in the fi eld of reproductive behaviour, the protection of motherhood and childhood. Compilations, manuals and magazines intended for women were the most important regulators of behaviour, determining acceptable norms and rules. Materials from sources of personal origin and oral history make it possible to clearly demonstrate the real feelings of women. The study of women’s everyday and daily life in the aspect related to pregnancy planning, bearing and raising children will allow us to compare the real situation and the course of implementation of tasks in the fi eld of maternal and child health. The demographic surge in the conditions of the economy reviving after the war, the lack of preschool institutions, as well as the low material wealth of most families, forced women to adapt to the situation. In the conditions of combining the roles of mother, wife and female worker, women entrusted themselves with almost overwork, which affected the health and well-being of the family. The procedure for legalising abortion gave women not only the right to decide the issue of motherhood themselves, but also made open the already necessary, but harmful to health, habitual way of birth control. Maternal care in diffi cult material and housing conditions became the concern of women and the older generation, who helped young women to combine the role of a working mother, which the country’s leadership confi dently assigned to women.

Download Full-text

Shuffling of Linear Orders

Canadian Mathematical Bulletin ◽

10.4153/cmb-1995-032-1 ◽

1995 ◽

Vol 38 (2) ◽

pp. 223-229

Author(s):

John Lindsay Orr

Keyword(s):

Ordered Set ◽

Linear Orders ◽

Real Numbers ◽

The Real ◽

Linearly Ordered Set

AbstractA linearly ordered set A is said to shuffle into another linearly ordered set B if there is an order preserving surjection A —> B such that the preimage of each member of a cofinite subset of B has an arbitrary pre-defined finite cardinality. We show that every countable linearly ordered set shuffles into itself. This leads to consequences on transformations of subsets of the real numbers by order preserving maps.

Download Full-text

A question of van den Dries and a theorem of Lipshitz and Robinson; Not everything is standard

Journal of Symbolic Logic ◽

10.2178/jsl/1174668387 ◽

2007 ◽

Vol 72 (1) ◽

pp. 119-122 ◽

Cited By ~ 4

Author(s):

Ehud Hrushovski ◽

Ya'acov Peterzil

Keyword(s):

Real Numbers ◽

The Real ◽

First Order ◽

Real Closed Fields ◽

Minimal Structure ◽

Closed Fields ◽

New Construction ◽

The Relationship

AbstractWe use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

Download Full-text

Effects of external trigeminal nerve stimulation (eTNS) on laser evoked cortical potentials (LEP): A pilot study in migraine patients and controls

Cephalalgia ◽

10.1177/0333102417728748 ◽

2017 ◽

Vol 38 (7) ◽

pp. 1245-1256 ◽

Cited By ~ 9

Author(s):

Eleonora Vecchio ◽

Eleonora Gentile ◽

Giovanni Franco ◽

Katia Ricci ◽

Marina de Tommaso

Keyword(s):

Pilot Study ◽

Nerve Stimulation ◽

Migraine Without Aura ◽

Anterior Cingulate ◽

Evoked Responses ◽

The Real ◽

Sham Stimulation ◽

Primary Headache Disorders ◽

Transcutaneous Nerve Stimulation ◽

The Right

Background Transcutaneous external supraorbital nerve stimulation has emerged as a treatment option for primary headache disorders, though its action mechanism is still unclear. Study aim In this randomized, sham-controlled pilot study we aimed to test the effects of a single external transcutaneous nerve stimulation session on pain perception and cortical responses induced by painful laser stimuli delivered to the right forehead and the right hand in a cohort of migraine without aura patients and healthy controls. Methods Seventeen migraine without aura patients and 21 age- and sex-matched controls were selected and randomly assigned to a real or sham external transcutaneous nerve stimulation single stimulation session. The external transcutaneous nerve stimulation was delivered with a self-adhesive electrode placed on the forehead and generating a 60 Hz pulse at 16 mA intensity for 20 minutes. For sham stimulation, we used 2 mA intensity. Laser evoked responses were recorded from 21 scalp electrodes in basal condition (T0), during external transcutaneous nerve stimulation and sham stimulation (T1), and immediately after these (T2). The laser evoked responses were analyzed by LORETA software. Results The real external transcutaneous nerve stimulation reduced the trigeminal N2P2 amplitude in migraine and control groups significantly in respect to placebo. The real stimulation was associated with lower activity in the anterior cingulate cortex under trigeminal laser stimuli. The pattern of LEP-reduced habituation was reverted by real and sham transcutaneous stimulation in migraine patients. Conclusions The present results could suggest that the external transcutaneous nerve stimulation may interfere with the threshold and the extent of trigeminal system activation, with a mechanism of potential utility in the resolution and prevention of migraine attacks.

Download Full-text

XXXIV. On the transit of Venus in 1769. To the Right Honourable The Earl of Morton, President to the Council and Fellows of the Royal Society, this discourse is, with all humility, inscribed, by their humble servant, Thomas Hornsby

Philosophical Transactions of the Royal Society of London ◽

10.1098/rstl.1765.0035 ◽

1765 ◽

Vol 55 ◽

pp. 326-344 ◽

Cited By ~ 1

Keyword(s):

Royal Society ◽

The Sun ◽

The Real ◽

The Earth ◽

Theory Of Gravity ◽

The Right ◽

Made In

The observations of the late transit of Venus, though made with all possible care and accuracy, have not enabled us to determine with certainty the real quantity of the sun's parallax; since, by a comparison of the observations made in several parts of the globe, the sun's parallax is not less than 8" 1/2, nor does it seem to exceed 10". From the labours of those gentlemen, who have attempted to deduce this quantity from the theory of gravity, it should seem that the earth performs its annual revolution round the sun at a greater distance than is generally imagined: since Mr. Professor Stewart has determined the sun's parallax to be only 6', 9, and Mr. Mayer, the late celebrated Professor at Gottingen, who hath brought the lunar tables to a degree of perfection almost unexpected, is of opinion that it cannot exceed 8".

Download Full-text

On expressible sets and p-adic numbers

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091509000091 ◽

2011 ◽

Vol 54 (2) ◽

pp. 411-422

Author(s):

Jaroslav Hančl ◽

Radhakrishnan Nair ◽

Simona Pulcerova ◽

Jan Šustek

Keyword(s):

Haar Measure ◽

Real Numbers ◽

The Real ◽

Expressible Set

AbstractContinuing earlier studies over the real numbers, we study the expressible set of a sequence A = (an)n≥1 of p-adic numbers, which we define to be the set EpA = {∑n≥1ancn: cn ∈ ℕ}. We show that in certain circumstances we can calculate the Haar measure of EpA exactly. It turns out that our results extend to sequences of matrices with p-adic entries, so this is the setting in which we work.

Download Full-text

DIRECTLY FINITE ALGEBRAS OF PSEUDOFUNCTIONS ON LOCALLY COMPACT GROUPS

Glasgow Mathematical Journal ◽

10.1017/s0017089514000573 ◽

2014 ◽

Vol 57 (3) ◽

pp. 693-707

Author(s):

YEMON CHOI

Keyword(s):

Invertible Element ◽

Locally Compact Groups ◽

Compact Groups ◽

Complex Line ◽

Locally Compact ◽

The Real ◽

C Algebra ◽

Finite Algebras ◽

Unimodular Group ◽

Reduced Group

AbstractAn algebraAis said to be directly finite if each left-invertible element in the (conditional) unitization ofAis right invertible. We show that the reduced group C*-algebra of a unimodular group is directly finite, extending known results for the discrete case. We also investigate the corresponding problem for algebras ofp-pseudofunctions, showing that these algebras are directly finite ifGis amenable and unimodular, or unimodular with the Kunze–Stein property. An exposition is also given of how existing results from the literature imply thatL1(G) is not directly finite whenGis the affine group of either the real or complex line.

Download Full-text