scholarly journals Differentiability properties of the family of p-parallel bodies

2016 ◽  
Vol 10 (1) ◽  
pp. 186-207 ◽  
Author(s):  
Hernández Cifre ◽  
Martínez Fernández ◽  
Saorín Gómez
Keyword(s):  
Lower Bound ◽  
Support Function ◽  
Classical Case ◽  
Parameter Family ◽  
The Family ◽  
Polynomial Expression ◽  
The One ◽  
Differentiability Properties ◽  
Sharp Lower Bound

We investigate the differentiability of the quermassintegrals with respect to the one-parameter family of the p-parallel bodies. As in the classical case, we obtain that the volume is always differentiable. Although there is no polynomial expression for a p-sum, the rest of quermassintegrals are differentiable on positive values of the parameter too. We prove a sharp lower bound for the derivative of the support function of the p-inner parallel bodies along with equality conditions.

Success probabilities for second guessers

1980 ◽  
Vol 17 (04) ◽  
pp. 1133-1137 ◽  
Author(s):  
A. O. Pittenger
Keyword(s):  
Lower Bound ◽  
Dimensional Space ◽  
Success Probability ◽  
First Person ◽  
True Location ◽  
Rotationally Symmetric ◽  
The One ◽  
Sharp Lower Bound

Two people independently and with the same distribution guess the location of an unseen object in n-dimensional space, and the one whose guess is closer to the unseen object is declared the winner. The first person announces his guess, but the second modifies his unspoken idea by moving his guess in the direction of the first guess and as close to it as possible. It is shown that if the distribution of guesses is rotationally symmetric about the true location of the unseen object, ¾ is the sharp lower bound for the success probability of the second guesser. If the distribution is fixed and the dimension increases, then for a certain class of distributions, the success probability approaches 1.

A mathematical model of the rotor profile of the single-screw compressor

2002 ◽  
Vol 216 (3) ◽  
pp. 343-351 ◽  
Author(s):  
S-C Yang
Keyword(s):  
Mathematical Model ◽  
Parameter Family ◽  
Cutting Edge ◽  
Screw Compressor ◽  
Single Screw ◽  
Rotor Profile ◽  
The Family ◽  
Screw Rotor ◽  
The One ◽  
Screw Rotors

This paper presents a method for determining the basic profile of a single-screw compressor including a gate rotor and a screw rotor. The inverse envelope concept for determining the cutting-edge curve of the gate rotor is presented. Based on this concept, the required cutter for machining the screw rotor can be obtained by an envelope of the one-parameter family of obtained screw rotors. The obtained screw rotor is an envelope of the family of gate rotor surfaces. Let the obtained envelope of the one-parameter family of gate rotor surfaces become the generating surface. The inverse envelope can be used to obtain the envelope of the family of generating surfaces. Then, the profile of the gate rotor with the cutting-edge curve can be easily obtained. The proposed method shows that the gate rotor and the screw rotor are engaged along the contact line at every instant. This is essential to reduce the effect of leakage on compressor performance. In this paper, a mathematical model of the meshing principle of the screw rotor with the gate rotor is established. As an example, the single-screw compressor for a compressor ratio of 11:6 is determined with the aid of the proposed mathematical model. Results from these mathematical models should have applications in the design of single-screw compressors.

scholarly journals Mating quadratic maps with the modular group II

2019 ◽  
Vol 220 (1) ◽  
pp. 185-210
Author(s):  
Shaun Bullett ◽  
Luna Lomonaco
Keyword(s):  
Modular Group ◽  
Parameter Family ◽  
Quadratic Polynomial ◽  
Complex Parameter ◽  
Rational Maps ◽  
Quadratic Maps ◽  
The Family ◽  
The One ◽  
Holomorphic Correspondences ◽  
Connectedness Locus

Abstract In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of (2 : 2) holomorphic correspondences $$\mathcal {F}_a$$Fa: $$\begin{aligned} \left( \frac{aw-1}{w-1}\right) ^2+\left( \frac{aw-1}{w-1}\right) \left( \frac{az+1}{z+1}\right) +\left( \frac{az+1}{z+1}\right) ^2=3 \end{aligned}$$aw-1w-12+aw-1w-1az+1z+1+az+1z+12=3and proved that for every value of $$a \in [4,7] \subset \mathbb {R}$$a∈[4,7]⊂R the correspondence $$\mathcal {F}_a$$Fa is a mating between a quadratic polynomial $$Q_c(z)=z^2+c,\,\,c \in \mathbb {R}$$Qc(z)=z2+c,c∈R, and the modular group $$\varGamma =PSL(2,\mathbb {Z})$$Γ=PSL(2,Z). They conjectured that this is the case for every member of the family $$\mathcal {F}_a$$Fa which has a in the connectedness locus. We show here that matings between the modular group and rational maps in the parabolic quadratic family $$Per_1(1)$$Per1(1) provide a better model: we prove that every member of the family $$\mathcal {F}_a$$Fa which has a in the connectedness locus is such a mating.

Success probabilities for second guessers

1980 ◽  
Vol 17 (4) ◽  
pp. 1133-1137 ◽  
Author(s):  
A. O. Pittenger
Keyword(s):  
Lower Bound ◽  
Dimensional Space ◽  
Success Probability ◽  
First Person ◽  
True Location ◽  
Rotationally Symmetric ◽  
The One ◽  
Sharp Lower Bound

Two people independently and with the same distribution guess the location of an unseen object in n-dimensional space, and the one whose guess is closer to the unseen object is declared the winner. The first person announces his guess, but the second modifies his unspoken idea by moving his guess in the direction of the first guess and as close to it as possible. It is shown that if the distribution of guesses is rotationally symmetric about the true location of the unseen object, ¾ is the sharp lower bound for the success probability of the second guesser. If the distribution is fixed and the dimension increases, then for a certain class of distributions, the success probability approaches 1.

Murder with Impunity: The Construction of Arab Masculinities and Honor Crimes

1970 ◽  
pp. 38-45
Author(s):  
May Abu Jaber
Keyword(s):  
Violence Against Women ◽  
Social Boundaries ◽  
Religious Institutions ◽  
The Social ◽  
The Family ◽  
The Media ◽  
The One ◽  
Male Authority ◽  
Cultural Networks ◽  
Gender Specific

Violence against women (VAW) continues to exist as a pervasive, structural,systematic, and institutionalized violation of women’s basic human rights (UNDivision of Advancement for Women, 2006). It cuts across the boundaries of age, race, class, education, and religion which affect women of all ages and all backgrounds in every corner of the world. Such violence is used to control and subjugate women by instilling a sense of insecurity that keeps them “bound to the home, economically exploited and socially suppressed” (Mathu, 2008, p. 65). It is estimated that one out of every five women worldwide will be abused during her lifetime with rates reaching up to 70 percent in some countries (WHO, 2005). Whether this abuse is perpetrated by the state and its agents, by family members, or even by strangers, VAW is closely related to the regulation of sexuality in a gender specific (patriarchal) manner. This regulation is, on the one hand, maintained through the implementation of strict cultural, communal, and religious norms, and on the other hand, through particular legal measures that sustain these norms. Therefore, religious institutions, the media, the family/tribe, cultural networks, and the legal system continually disciplinewomen’s sexuality and punish those women (and in some instances men) who have transgressed or allegedly contravened the social boundaries of ‘appropriateness’ as delineated by each society. Such women/men may include lesbians/gays, women who appear ‘too masculine’ or men who appear ‘too feminine,’ women who try to exercise their rights freely or men who do not assert their rights as ‘real men’ should, women/men who have been sexually assaulted or raped, and women/men who challenge male/older male authority.

The least distance between extremums and minimal period of solutions to autonomous vector differential equations

2019 ◽  
Vol 485 (2) ◽  
pp. 142-144
Author(s):  
A. A. Zevin
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Lipschitz Constant ◽  
Minimal Period ◽  
Arbitrary Vector ◽  
Vector Norm ◽  
Sharp Lower Bound

Solutions x(t) of the Lipschitz equation x = f(x) with an arbitrary vector norm are considered. It is proved that the sharp lower bound for the distances between successive extremums of xk(t) equals π/L where L is the Lipschitz constant. For non-constant periodic solutions, the lower bound for the periods is 2π/L. These estimates are achieved for norms that are invariant with respect to permutation of the indices.

scholarly journals Personality and Dementia: an Approach to Differential Profile of the Caregiver

2011 ◽  
Vol 1 (3) ◽  
pp. 85-94
Author(s):  
Elena de Andrés-Jiménez ◽  
Rosa Mª Limiñana-Gras ◽  
Encarna Fernández-Ros
Keyword(s):  
Relevant Information ◽  
Personality Profile ◽  
Family Carers ◽  
Psychological Variables ◽  
People With Dementia ◽  
The Family ◽  
Study Population ◽  
The One ◽  
The Impact

The aim of this study is to determine the existence of a characteristic personality profile of family carers of people with dementia. The correct knowledge and use of psychological variables which affect the carer, helps to promote appropriate actions to mitigate the impact of care and improve the carer’s quality of life and likewise the one of the person cared for. The study population consists of 69 family carers of people with dementia, members of various associations and care centers. The results allow us to identify a characteristic personality profile for these carers and it reveals a specific psychological working in this sample, although we cannot directly relate it with the tasks of caring for people with this disease, this profile gives us very relevant information to pay more attention to the needs of this group. Moreover, the analysis of personality styles depends on the sex of the family carer, showing, once again, that the woman is in a situation of most vulnerability.

scholarly journals Compactness and Sharp Lower Bound for a 2D Smectics Model

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Michael Novack ◽  
Xiaodong Yan
Keyword(s):  
Lower Bound ◽  
Sharp Lower Bound
Sign in / Sign up

Export Citation Format

Share Document