scholarly journals Tips of tongues in the double standard family*

Nonlinearity ◽  
2021 ◽  
Vol 34 (12) ◽  
pp. 8174-8191
Author(s):  
Kuntal Banerjee ◽  
Xavier Buff ◽  
Jordi Canela ◽  
Adam Epstein
Keyword(s):  
Double Standard ◽  
Circle Maps ◽  
Multiple Zero ◽  
Standard Family ◽  
The Family ◽  
Local Coordinates ◽  
Alpha Beta

Abstract We answer a question raised by Misiurewicz and Rodrigues concerning the family of degree two circle maps F λ : R / Z → R / Z defined by F λ ( x ) ≔ 2 x + a + b π sin ( 2 π x ) with λ ≔ ( a , b ) ∈ R / Z × ( 0 , 1 ) . We prove that if F λ ◦ n − i d has a zero of multiplicity three in R / Z , then there is a system of local coordinates ( α , β ) : W → R 2 defined in a neighborhood W of λ, such that α(λ) = β(λ) = 0 and F μ ◦ n − i d has a multiple zero with μ ∈ W if and only if β 3(μ) = α 2(μ). This shows that the tips of tongues are regular cusps.

scholarly journals Reducing risk factors in overweight adult users of the family health strategy of the Distrito Federal

2013 ◽  
Vol 26 (6) ◽  
pp. 659-668 ◽  
Author(s):  
Caroline Romeiro ◽  
Júlia Aparecida Devidé Nogueira ◽  
Eliane Said Dutra ◽  
Kênia Mara Baiocchi de Carvalho
Keyword(s):  
Waist Circumference ◽  
Fasting Blood Glucose ◽  
Family Health ◽  
Lifestyle Changes ◽  
Control Group ◽  
Standard Family ◽  
Health Strategy ◽  
The Family ◽  
Family Health Strategy ◽  
Distrito Federal

OBJECTIVE: To evaluate the results of a multidisciplinary program to promote healthy habits on anthropometric and biochemical parameters on participants of the Family Health Strategy of the Distrito Federal. METHODS: The sample consisted of 279 overweight and obese adults of both sexes divided into two groups: intervention (IG, n=198) and control group (CG, n=89). The IG received standard Family Health Strategy care plus a multidisciplinary health promoting program that included dietary interventions and physical activity, called Set Waist Program. The control group received only standard ESF care. Data were collected at baseline and after 4 and 8 months of follow up. Body mass index, waist circumference, fasting blood glucose and lipid profile were assessed. RESULTS: Prevalence of obesity (63.3% to 49.4%, p=0.027) and waist circumference (102.2cm to 94.8cm, p<0.0001) were significantly reduced in IG. Total cholesterol, LDL and HDL-cholesterol were reduced in both groups. CONCLUSION: Reductions in anthropometric measures were maximized through simple interventions that stimulated lifestyle changes. These results suggest that multidisciplinary initiatives such the Set Waist Program can be incorporated into other Family Health Strategy teams to optimize the control of obesity and health promotion. Participant compliance is an issue that deserves further investigation.

LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY

1995 ◽  
Vol 05 (03) ◽  
pp. 673-699 ◽  
Author(s):  
NÚRIA FAGELLA
Keyword(s):  
Cross Sections ◽  
Julia Set ◽  
Three Dimensional ◽  
Mandelbrot Set ◽  
Dimensional Parameter ◽  
Quadratic Polynomials ◽  
New Family ◽  
Standard Family ◽  
The Family ◽  
Characteristic Features

The complexification of the standard family of circle maps Fαβ(θ)=θ+α+β+β sin(θ) mod (2π) is given by Fαβ(ω)=ωeiαe(β/2)(ω−1/ω) and its lift fαβ(z)=z+a+β sin(z). We investigate the three-dimensional parameter space for Fαβ that results from considering a complex and β real. In particular, we study the two-dimensional cross-sections β=constant as β tends to zero. As the functions tend to the rigid rotation Fα,0, their dynamics tend to the dynamics of the family Gλ(z)=λzez where λ=e−iα. This new family exhibits behavior typical of the exponential family together with characteristic features of quadratic polynomials. For example, we show that the λ-plane contains infinitely many curves for which the Julia set of the corresponding maps is the whole plane. We also prove the existence of infinitely many sets of λ values homeomorphic to the Mandelbrot set.

scholarly journals LOWER BOUND TO A PROBLEM OF MOCANU ON DIFFERENTIAL SUBORDINATION

1997 ◽  
Vol 27 (3) ◽  
pp. 209-217
Author(s):  
S. PONNUSAMY
Keyword(s):  
Lower Bound ◽  
Analytic Functions ◽  
Unit Disc ◽  
Differential Subordination ◽  
The Family ◽  
Alpha Beta ◽  
Starlike Mappings

Let $s^*$ denote the family of starlike mappings in the unit disc $\Delta$. Let $\mathcal{R}(\alpha, \beta)$ denote the family of normalized analytic functions in $\Delta$ satisfying the condition Re$(f'(z)+\alpha f''(z))>\beta$, $z \in\Delta$ for some $\alpha > 0$. In this note, among other things, we give a lower bound to the problem of Mocanu aimed at determining $\inf\{\alpha : \mathcal{R}(\alpha,0) \subset S^*\}$.

Lines, circles, focal and symmetry sets

1995 ◽  
Vol 118 (3) ◽  
pp. 411-436 ◽  
Author(s):  
J. W. Bruce
Keyword(s):  
Differential Geometry ◽  
Singularity Theory ◽  
Geometric Invariant ◽  
Circle Maps ◽  
Bifurcation Set ◽  
General Theme ◽  
Smooth Family ◽  
The Family ◽  
Parameter Values

Let X be a surface in Euclidean 3-space, hereafter denoted by ℝ3. In the paper [13] Montaldi considered the contact of the surface X with circles, and obtained some very attractive results. In this piece of work we want to address some more detailed questions concerning such contact. In keeping with a general theme within singularity theory we shall bundle the circles up into fibres of certain maps and consider the restriction of these mappings to our surface X. In other words we shall be interested in the simultaneous contact of the surface X with special families of circles. The particular families we shall consider are parameterized by the set K of all lines in ℝ3; associated to such a line we have the family of all circles lying in planes orthogonal to the line, and centred on the line. The line will be referred to as the axis of the circle. Suppose, for example, the line in question is given by x1 = x2 = 0. We can consider the map ℝ3 → ℝ2 given by . The fibres of this mapping are clearly the set of circles with the properties described above together, of course, with single points on the line itself. So the family of oriented lines parameterizes a family of mappings ℝ3 → ℝ2, and by restriction a family of mappings X → ℝ2. It is of interest to relate the singularities of this mapping to the differential geometry of X. The key geometric invariant of any smooth family is its bifurcation set, that is the set of parameter values for which the corresponding map fails to be stable. We shall see that for the family of circle maps the bifurcation set is of some interest.

Bifurcations of dynamic rays in complex polynomials of degree two

1992 ◽  
Vol 12 (3) ◽  
pp. 401-423 ◽  
Author(s):  
Pau Atela
Keyword(s):  
Fixed Points ◽  
Julia Set ◽  
Period Doubling ◽  
Mandelbrot Set ◽  
Complex Polynomials ◽  
Circle Maps ◽  
External Rays ◽  
The Family ◽  
Parameter Values ◽  
Dynamic Plane

AbstractIn the study of bifurcations of the family of degree-two complex polynomials, attention has been given mainly to parameter values within the Mandelbrot set M (e.g., connectedness of the Julia set and period doubling). The reason for this is that outside M, the Julia set is at all times a hyperbolic Cantor set. In this paper weconsider precisely this, values of the parameter in the complement of M. We find bifurcations occurring not on the Julia set itself but on the dynamic rays landing on itfrom infinity. As the parameter crosses the external rays of M, in the dynamic plane the points of the Julia set gain and lose dynamic rays. We describe these bifurcations with the aid of a family of circle maps and we study in detail the case of the fixed points.

Sexual and Premarital Attitudes of Iranian College Students

1985 ◽  
Vol 57 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Reza Shapurian ◽  
Mohammadreza Hojat
Keyword(s):  
College Students ◽  
Double Standard ◽  
Premarital Sex ◽  
Sexual Morality ◽  
Islamic Revolution ◽  
Iranian Women ◽  
Sexual Freedom ◽  
Men And Women ◽  
Attitude Inventory ◽  
The Family

To study the similarities as well as differences in the sexual and premarital attitudes of the younger Iranian men and women and Western students, a Persian revision of the attitude inventory used by Schofield was given to a sample of Iranian college students (199 men and 193 women) prior to the onset of Islamic revolution in this country. Present findings confirm, as expected, similarities on some dimensions as well as differences on others between Iranian men and women and between Iranian and British samples in Schofield's study. Iranian men and women differed significantly on their attitudes towards premarital sex for men as indicated by a higher percentage of women who agreed on premarital sex for male peers but not for Iranian women. The Iranian sample compared with their British peers represented more conservative sexual and more traditional premarital attitudes as indicated by a higher proportion of agree-responses to statements such as a bad reputation would result from premarital sex for women or sexual freedom leads to trouble. A double standard of sexual morality was found among Iranian subjects, virginity was given a high value, and loyalty to the family was considered important.

scholarly journals Equicontinuity of iterates of circle maps

1998 ◽  
Vol 21 (3) ◽  
pp. 453-458 ◽  
Author(s):  
Antonios Valaristos
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Circle Maps ◽  
Continuous Map ◽  
The Family ◽  
Necessary And Sufficient

Letfbe a continuous map of the circle to itself. Necessary and sufficient conditions are given for the family ofiterates{fn}n=1∞to be equicontinuous.

scholarly journals Loewner evolution of hedgehogs and 2-conformal measures of circle maps

2020 ◽  
pp. 1-20
Author(s):  
KINGSHOOK BISWAS
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Unit Disk ◽  
Infinitesimal Generator ◽  
Acta Math ◽  
Loewner Equation ◽  
Circle Maps ◽  
Loewner Evolution ◽  
The Family ◽  
Conformal Measures

Abstract Let f be a germ of a holomorphic diffeomorphism with an irrationally indifferent fixed point at the origin in $${\mathbb C}$$ (i.e. $$f(0) = 0, f'(0) = e^{2\pi i \alpha }, \alpha \in {\mathbb R} - {\mathbb Q}$$ ). Pérez-Marco [Fixed points and circle maps. Acta Math.179(2) (1997), 243–294] showed the existence of a unique continuous monotone one-parameter family of non-trivial invariant full continua containing the fixed point called Siegel compacta, and gave a correspondence between germs and families $$(g_t)$$ of circle maps obtained by conformally mapping the complement of these compacts to the complement of the unit disk. The family of circle maps $$(g_t)$$ is the orbit of a locally defined semigroup $$(\Phi _t)$$ on the space of analytic circle maps, which we show has a well-defined infinitesimal generator X. The explicit form of X is obtained by using the Loewner equation associated to the family of hulls $$(K_t)$$ . We show that the Loewner measures $$(\mu _t)$$ driving the equation are 2-conformal measures on the circle for the circle maps $$(g_t)$$ .

Analytic iterations on Riemann surfaces

1969 ◽  
Vol 1 (2) ◽  
pp. 183-194
Author(s):  
Meira Lavie
Keyword(s):  
Differential Equation ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Analytic Family ◽  
Analytic Manifold ◽  
Analytic Group ◽  
The Family ◽  
Local Coordinates ◽  
Analytic Iteration ◽  
Abstract Riemann Surface

A complex analytic family of mappings P → M(α, P) from an abstract Riemann surface (analytic manifold) into itself is studied. The mapping M(α, P) is assumed to satisfy in local coordinates the autonomous differential equation = L(w), and the condition M(O, P) = P. Under certain assumptions of regularity of the reciprocal differential L in a domain D ⊂ S, we prove that for every fixed α, ∣a∣ < α, the mapping M(α, P) is conformal and one to one in D. Moreover, it is shown that the family of mappings M(α, P) satisfies the iteration equation M[a, M(b, P)] = M(a + b, P) and hence is an analytic group (analytic iteration).

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