The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.

A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Investigation into the impact of embedded generators on distribution system performance using theorem of superposition

Since the 1980s, huge efforts have been made to utilise renewable energy sources to generate electric power. One of the interesting issues about embedded generators is the question of optimal placement and sizing of the embedded generators. This paper reports an investigation of impact of the integration of embedded generators on the overall performances of the distribution networks in the steady state, using theorem of superposition. Set of distribution system indices is proposed to observe performances of the distribution networks with embedded generators. Results obtained from the case study using IEEE test network are presented and discussed.

Charge density alterations in human hair fibers: An investigation using electrostatic force microscopy

A new method for high-resolution analyses of hair surface charge density under ambient conditions is presented in this paper. Electrostatic force microscopy (EFM) is used here to analyze changes in surface charge density in virgin hair, bleached hair, and hair treated with a cationic polymer. The atomic force microscopy technique is used concomitantly to analyze morphological changes in hair roughness and thickness. The EFM images depict exactly how the polymer is distributed on the surface of the hair fiber. The EFM's powerful analytical tools enabled us to evaluate the varying degrees of interaction between the hair fiber surface charge density and the cationic polymer. The surface charge density and the polymer's distribution in the hair fibers are presented in the light of EFM measurements. © 2006 Society of Cosmetic Scientists and the Socièété Française de Cosmétologie.

Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

A 12-month follow-up of hypopigmentation after laser hair removal

Introduction: Laser hair removal is becoming an increasingly popular alternative to traditional methods such as shaving, waxing, among other methods. Semiconductor diode lasers are considered the most efficient light sources available and are especially well suited for clinical applications including hair reduction. The effectiveness of laser hair reduction depends on many variables, including the skin type of the patient. Material and Methods: A patient with Fitzpatrick Skin Type IV was submitted to laser hair removal of the arms with a high-power diode laser system with long pulses with a wavelength of 800 nm, a fluence of 40 J/cm2 and a pulse width of 20 ms. A 12-month follow-up assessment was performed and included photography and questionnaire. Results: Hypopigmentation was observed after a single laser hair removal section. After 6 months with the area totally covered, a gradual suntan with a sun screen lotion with an SPF of 15 was prescribed by the dermatologist. After 12 months of the initial treatment, a complete recovery of the hypopigmentation was achieved. Conclusion: Although a safe procedure, lasers for hair removal may be associated with adverse side effects including undesired pigment alterations. Before starting a laser hair removal treatment, patients seeking the eradication of hair should be informed that temporary, and possibly permanent, pigmentary changes may occur. © 2013 Informa UK, Ltd.

Is characterizing the digital forensic facial reconstruction with hair necessary? A familiar assessors' analysis

Background: In the international scientific literature, there are few studies that emphasize the presence or absence of hair in forensic facial reconstructions. There are neither Brazilian studies concerning digital facial reconstructions without hair, nor research comparing recognition tests between digital facial reconstructions with hair and without hair. The miscegenation of Brazilian people is considerable. Brazilian people, and, in particular, Brazilian women, even if considered as Caucasoid, may present the hair in very different ways: curly, wavy or straight, blonde, red, brown or black, long or short, etc. For this reason, it is difficult to find a correct type of hair for facial reconstruction (unless, in real cases, some hair is recovered with the skeletal remains). Aims and methods: This study focuses on the performance of three different digital forensic facial reconstructions, without hair, of a Brazilian female subject (based on one international database and two Brazilian databases for soft facial-tissue thickness) and evaluates the digital forensic facial reconstructions comparing them to photographs of the target individual and nine other subjects, employing the recognition method. A total of 22 assessors participated in the recognition process; all of them were familiar with the 10 individuals who composed the face pool. Results and conclusions: The target subject was correctly recognized by 41% of the 22 examiners in the International Pattern, by 32% in the Brazilian Magnetic Resonance Pattern and by 32% in the Brazilian Fresh Cadavers Pattern. The facial reconstructions without hair were correctly recognized using the three databases of facial soft-tissue thickness. The observed results were higher than the results obtained using facial reconstructions with hair, from the same skull, which can indicate that it is better to not use hair, at least when there is no information concerning its characteristics. © 2013 Elsevier B.V. All rights reserved.

Performance, survivability and carcass traits of crossbred lambs from five paternal breeds with local hair breed Santa Inês ewes

The present study aimed to evaluate the performance, survivability and carcass traits of crossbred lambs. Data from 299 lambs born to 209 ewes were used. The dams were from a local hair breed (Santa Inês) and five breeds of sires were used: Dorper (DR), Ile de France (IF), Hampshire Down (HD), Texel (TX) and Santa Inês (SI). The lambs were weighed at birth, weaning and slaughter. Fasting body weight, skin thickness, hot and cold carcass weight, carcass yield and carcass length were measured at slaughter. Carcasses were separated into commercial cuts: neck, shoulder, rib, belly, loin and leg. Leg length and circumference were measured. Analyses of variances using MIXED procedure in SAS® were carried out for weights and carcass traits. Factor, discriminant and canonical analysis were carried out. Mortality data of animals from birth until slaughter was analyzed using logistic regression. The HD animals had the highest mortality rate. TX lambs had similar growth rate and survivability compared to DR and IF and had better carcass traits than these genetic groups. Therefore, this breed can be used as paternal breed to crossbreeding with Santa Inês dams. Santa Inês animals did not differ in growth from birth until slaughter compared to crossbred animals, which highlights the potential of this naturalized breed for meat production. Moreover, there is a great variability inside this breed for carcass and growth traits which may undergo great improvement through selection programs. © 2013 Elsevier B.V.

Towards an insight on photodamage in hair fibre by UV-light: An experimental and theoretical study

Synopsis: Objectives: In this research, an experimental and theoretical study was conducted to design a photodegradation mechanism of the amino acid tryptophan (Trp) in hair fibres. Methods: For the experimental research, Caucasian hair fibres were exposed to several different solar radiation simulation periods. Then, Trp and its photoproducts (N-formylkynurenine and kynurenine) were assayed by excitation and emission spectroscopic analysis. Results: For the theoretical study, reactions involved in the photodegradation of Trp were evaluated by high-level quantum mechanical calculations in a density functional theory (DFT) framework which indicate a probable Trp degradation mechanism with a minimum expended energy pathway. Conclusion: The biochemistry concerning these reactions is essentially important for a biological system where the degradation of Trp occurs. © 2013 John Wiley & Sons Ltd.

Development and sensory analysis of shampoo for curly hair

Objective: This study aimed to compare the sensory performance of a shampoo formulation with Polyurethane-14, AMP-acrylates copolymer (PAAC) in relation to control formulation in curly and natural hair tresses. Methods: Curly and natural hair tresses (n = 8) of equal size and weight were pre-treated by washing with a standard shampoo. After the hair tresses were treated with a formulation containing polymer (formulation A) and compared to hair tresses treated with control formulation (Formulation B). Each panelist (n=2) is asked to indicate which tress performs better for each of seven sensory attributes evaluated (quantity and creamy foam, combing, wet touch, frizz formation, curl definition and volume). It was collected images of hair tresses at 0, 1, 2, 4 and 24 hours of washing, comparing the attributes: volume, frizz formation and curl definition. The results were analyzed using table to test of paired assessment, being: SUPERIOR results - 8 and 7 positive evaluations; SIMILAR results - 2 to 6 positive evaluations; INFERIOR results - 1 and 0 positive evaluations. Results: The addition of the PAAC on the shampoo formulation provided definition and modeling of curls, reducing volume and frizz in 24 hours. There was also lower foam formation in the formulation with polymer PAAC. However, it is important to note that this attribute has inversely proportional effect to the creamy foam, since more creamy foam, smaller quantity. Conclusions: It was concluded that the shampoo developed was effective in defining and modeling curl in natural and curly hair.

Peixoto's Theorem for vector fields on S2 with impasse points

The structural stability of vector fields with impasse regular curves on S2 is studied and a version of Peixoto's Theorem is established. Moreover a global analysis of normal forms of the constrained systems. A(x).ẋ=F(x),x∈R3,A∈M(3),F:R3→R3 in the Poincaré ball (i.e. in the compactification of R3 with the sphere S2 of the infinity) is made. © 2013 Elsevier Masson SAS.