Distributional chaos for weighted translation operators on groups

In this paper, we initiate the study of distributional chaos for weighted translations on locally compact groups, and give a sufficient condition for such operators to be distributionally chaotic. We also investigate the set of distributionally irregular vectors of weighted translations from the views of modulus, cone, equivalent class and atom. In particular, we show that the set of distributionally irregular vectors is residual if the group is the integer. Besides, the equivalent class of distributionally irregular vectors is path connected if the field is complex

Chaotic translations on weighted Orlicz spaces

Let $G$ be a locally compact group, $w$ be a weight on $G$ and $\Phi$ be a Young function. We give some characterizations for translation operators to be topologically transitive and chaotic on the weighted Orlicz space $L_w^\Phi(G)$. In particular, transitivity is equivalent to the blow-up/collapse property in our case. Moreover, the dense set of periodic elements implies transitivity automatically

Preparation And Characterization Of Water-Soluble Chitosan Gel For Skin Hydration.

Kitosan, biopoliaminosakarida secara linear dan semulajadi, telah mendapat banyak perhatian sebagai bio-polimer berfungsi dengan aplikasi dalam bidang farmaseutikal, makanan, kosmetik dan perubatan. Chitosan, a natural and linear biopolyaminosaccharide, has received much attention as a functional biopolymer with applications in pharmaceuticals, food, cosmetics and medicines. Nevertheless, chitosan application is limited by its solubility in aqueous solution

Breast Recontouring

The breast is an important structure of the human body in terms of function and esthetics. Derangements in breast mount—breast form/volume/profile/silhouette and nipple-areolar complex—size/shape/nipple projection are all concerns for not only females but also males. Simply esthetic problems of breasts encompass hypoplasia, atrophy, displacement of nipple-areolar complex, widened areola, redundant nipple, breast ptosis, macromastia, etc. Congenital anomalies of breast—Poland syndrome, pectus excavatum, pectus carinatum, etc.—all need to be taken care for restructuring of the body contour. Nowadays, breast cancer of different stages may need different reconstruction modality. Postmastectomy breast reconstruction is another big issue for plastic surgeons. This chapter on breast recontouring will address on every specific kind of breast contour disorders and imperfection, along with individualized strategies of refining, restoring, and reconstruction approaches

Improved Lower Bounds on the Domination Number of Hypercubes and Binary Codes with Covering Radius One

A dominating set on an $n$-dimensional hypercube is equivalent to a binary covering code of length $n$ and covering radius 1. It is still an open problem to determine the domination number $\gamma(Q_n)$ for $n\geq9$ and $n\ne2^{k},2^{k}-1$ ($k\in\mathbb{N}$). When $n$ is a multiple of 6, the best known lower bound is $\gamma(Q_n)\geq \frac{2^n}{n}$, given by Van Wee (1988). In this article, we present a new method using congruence properties due to Laurent Habsieger (1997) and obtained an improved lower bound $\gamma(Q_n)\geq \frac{(n-2)2^n }{n^2-2n-2}$.Comment: 13 pages, 1 figure, to be publishe

A Generalization of Bell Polynomials and Multinomial Expansions via Permutations on Partitions, by Perturbation expansions of Functional Determinants

We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type theorems in many sense. In particular, we give the new formulas as the double counting of Bell polynomial, Binomial Theorem and Multinomial Theorem.Comment: 17 page

Poincar\'e Gauge Theory With Coupled Even And Odd Parity Dynamic Spin-0 Modes: Dynamic Equations For Isotropic Bianchi Cosmologies

We are investigating the dynamics of a new Poincar\'e gauge theory of gravity model, which has cross coupling between the spin-0$^+$ and spin-0$^-$ modes. To this end we here consider a very appropriate situation---homogeneous-isotropic cosmologies---which is relatively simple, and yet all the modes have non-trivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these models lead to a set of first order equations that are compatible with those found for the FLRW models and provide a foundation for further investigations. Typical numerical evolution of these equations shows the expected effects of the cross parity coupling.Comment: 13 pages, 2 figure

Analytical approach of late-time evolution in a torsion cosmology

In this letter, we study the late-time evolution of a torsion cosmology only with the spin-$0^+$ mode. We find three kinds of analytical solutions with a constant affine scalar curvature. In the first case, it is not physical because the matter density will be negative. In the second case, it shows that the dark energy can be mimicked in the torsion cosmological model. In the third case, the characteristic of late-time evolution is similar to that of the universe of matter dominant. And we also find a kind of expression with the non-constant curvature that the periodic character of numerical calculation is only the reflection of solution in a specific period of evolution. Using these expressions, we shall be able to predict the evolution over the late-time. From this prediction, we know the fate of universe that the universe would expand forever, slowly asymtotically to a halt.Comment: 12pages,6 figure