Likely Limit Sets of a Class of p-order Feigenbaum's Maps

A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.

On Limit Sets and Discreteness Criteria for Nonelementary Subgroups of M(~n)

In this paper, we will study the nonelementary groups of MSbius transformations in R^n and some properties are obtained. Also in this paper we will prove several theorems about discreteness criteria and group convergence of nonelementary groups of M（R^n）.

Access to novel anti-diabetic agents in resource limited settings:A brief commentary

The prevalence of diabetes mellitus is increasing in resource limited settings.Simultaneously,there has been an increase in the number of novel therapies for the management of diabetes mellitus.However,use of novel antidiabetic therapies is limited because of major market access challenges in resource limited settings.Niching products to those patients with the highest absolute risk for major adverse cardiovascular outcomes,and thus most likely to benefit from the therapy,are less likely to have negative budget impact for funders.To improve access,and reduce morbidity and mortality,requires alignment amongst key stakeholders including patient advocacy groups,health care professional councils,national departments of health,the pharmaceutical industry,treasury and finance departments.

Exclusive Fibula Osteosynthesis for Treating Open Fractures Gustillo I-III B of the Distal Half of the Leg Bones in a Resources-Limited Setting

Introduction: Management of open leg bones fractures is a challenging health issue for the surgeon, particularly true in resource-limited settings. In this study, we evaluate exclusive fibular osteosynthesis in the treatment of open fractures of the distal half of the leg bones as a therapeutic option in our context. Methods: This is a prospective, experimental, multicenter study of 30 open fractures of the distal half of the leg bones treated with exclusive fibula osteosynthesis, conducted in 3 hospitals in the DRC from January 1, 2013 to September 30, 2016. Results: The age range of 20 to 40 years grouped 22 (73.4%) patients, the sex ratio was 1:1 and the unemployed were the most involved with 16 (53.3%) cases. The Gustilo II, I, III B and III A types represented 40%, 33.3%, 20% and 6.7%, respectively. The fractures were located in the distal third in 12 (40%) cases, in the middle third in 11 (36.7%) cases, and in both malleoli in 7 cases (23.3%). Osteosynthesis of the fibula by screw plate was applied in 22 (73.3%) patients and pinning in 8 (26.7%). Satisfactory reduction of the tibial fracture site was achieved in 29 (96.7%) cases and 100% bone healing was achieved within an average of 10 weeks. Four (13.3%) loss of alignment, 1 (3.3%) infection, 1 (3.3%) skin necrosis and 2 (6.7%) ankle stiffness complicated our fractures. Conclusion: Exclusive osteosynthesis of the fibula as a common technique for fractures of the distal half of the leg bones allowed us to reduce, immobilize and consolidate the tibial fracture in the required time and to preserve the mobility of the ankle.

COMPLEXITY OF LIMIT LANGUAGE OF THE ELEMENTARY CELLULAR AUTOMATON OF RULE 22

In this paper, the limit set of the elementary cellular automaton of rule 22 is considered. The limit language is defined from limit set and its complexity is studied by using formal language theory. It is proved that this language is not a regular language. This result shows that the dynamics of this cellular automaton is actually complicated.

Accurate equilibrium inversion barrier of ammonia by extrapolation to the one-electron basis set limit

A scheme based on treating uniform singlet-pair and triplet-pair interactions is suggested to extrapolate electron correlation energy of ammonia, calculated at two basis-set levels of ab initio theory in the infinite one-electron basis-set limit. The dual-level method is tested on the extrapolation of the full correlation in coupled-cluster singles and doubles and in the case also a noniterative perturbative correction for connected triple energies for the C3v and D3h structures of ammonia, with correlation-consistent basis sets of the type cc-pVXZ （X = D, T, Q, 5, 6） and aug-cc-pVXZ （X = D, T, Q, 5）. For testing and comparison purposes, the energies reported by Klopper [J. Comput. Chem. 22 1306 （2001）] have been taken. From a corresponding extrapolation of CCSD（T）/AVXZ energies for X = 4, 5, we obtain total inversion barriers of 1833.87 cm-1/1832.33 cm^-1 for the two/three-parameter extrapolation rules, which are in good agreement with other theoretical extrapolation and empirical values in the literature.

Fountain Set Limited Launched New Products of 2011 Autumn-Winter Collections:Eco-friendliness and Multi-category

Fountain Set Limited announced that its branch brand'Fountain Set' was producing 2011 autumn-winter collections on the 2010 Intertextile Shanghai Apparel Fabrics Trade Fair,displaying new products

Some Properties of Homogeneous Vector Fields

For planar analytic homogcneous vector fields, the existence of periodic orbits and the noncxistence of limit sets arc verilied. It is concluded that spacial analytic homlogencous vector tleld of order in has no limit sets for any m>1. Similar results arc extended to highel-dimensional polynomial homogeneous vector fields under certain conditions.

Stability Analysis of Nonsymmetric Cellular Neural Networks

This paper describes the problem of stability for one-dimensional Cellular Neural Networks（CNNs）. A sufficient condition is presented to ensure complete stability for a class of special CNN＇s with nonsymmetric templates, where the parameter in the output function is greater than or equal to zero. The main method is analysising the property of the equilibrium point of the CNNs system.

Basis Set Extrapolation for the High Resolution Spectroscopy

Valence and all electron correlation energies of a large set of atoms and molecules with structural motifs from amino acids and peptides at their equilibrium as well as non-equilibrium geometries are calculated at the levels of MP2, RI-MP2, and CCSD （T） with Dunnings sequential correlation consistent basis sets. A two point basis set extrapolation scheme for correlation energies to the complete basis set limit based on only DZ （double-zeta） and TZ （triple-zeta） results is presented and analyzed. We show that this basis set extrapolation scheme reduces the computational cost by two to three orders of magnitude to obtain the same accuracy as simpler extrapolations from higher order basis set computations.

Limit Set Problem of Multi-Agent Systems with Finite States: An Eigenvalue-Based Approach

This paper studies the limit set of multi-agent system with finite states, in which the system is converted into a linear system through an expansion of space. Then, the structure properties of the system matrix are investigated, and the relationships between the eigenvalues and the limit set are developed. As an application, the nilpotent problem of elementary cellular automata(ECA) known as algorithmically undecidable is considered, and all the nilpotent ECA are found out which consists of rules 0, 8, 64, 239, 253, 255.

Attractor, chain recurrent set and limit set of flow

The properties of attractor, chain recurrent set and limit set of the flow on a compact metric space are studied.

On Dynamics of Infinitely Generated Contractive Mapping Systems on pZ_p

Let p≥2 be a prime number and Zp be the ring of p-adic intergers.Let G be a semigroup generated by infinitely many contractive maps on p Zp.It is shown that if G satisfies the open tiling conditions,then there exists a shift transformation on the limit set of G and the shift transformation is ergodic with respect to the Haar measure on p Zp.As an application,we can generalize p-adic Khinchin’s Theorem and p-adic Lochs’Theorem to any infinitely generated semigroup by use of the ergodicity of the shift transformation.

Challenges in initiating antiretroviral therapy for all HIV-infected people regardless of CD4 cell count

Introduction:Recently published large randomized controlled trials,START,TEMPRANO and HPTN 052 show the clinical benefit of early initiation of antiretroviral treatment(ART)in HIV-infected persons and in reducing HIV transmission.The trials influenced the World Health Organization(WHO)decision to issue updated recommendations to prescribe ART to all individuals living with HIV,irrespective of age and CD4 cell count.Discussion:It is clear that the new 2015 WHO recommendations if followed,will change the face of the HIV epidemic and probably curb its burden over time.Implementation however,requires that health systems,especially those in low and middle-income settings,be ready to face this challenge on a large scale.HIV prevention and treatment are easy in theory yet hard in practice.The new WHO guidelines for initiation of ART regardless of CD4 cell count will lead to upfront increases in the costs of healthcare delivery as the goal is to treat all those now newly eligible for ART.Around 22 million people living with HIV qualify and will therefore require ART.Related challenges immediately follow:firstly,that everyone must be tested for HIV;secondly,that anyone who has had an HIV test should know their result and understand its significance;and,thirdly,that every person identified as HIV-positive should receive and remain on ART.The emergence of HIV drug resistant strains when treatment is started at higher CD4 cell count thresholds is a further concern as persons on HIV treatment for longer periods of time are at increased risk of intermittent medication adherence.Conclusions:The new WHO recommendations for ART are welcome,but lacking as they fail to consider meaningful solutions to the challenges inherent to implementation.They fail to incorporate actual strategies on how to disseminate and adopt these far-reaching guidelines,especially in sub-Saharan Africa,an area with weak healthcare infrastructures.Well-designed,high-quality research is needed to assess the feasibility,safety,acceptability,impact,and cost of innovations such as the universal voluntary testing and immediate treatment approaches,and broad consultation must address community,human rights,ethical,and political concerns.

TRAJECTORY TRACKING THEORY OF QUANTUM SYSTEMS

The orbit tracking problem of a free-evolutionary target system in closed quantum systems is solved by changing it into the state transferring problem with the help of unitary transformation.The control law designed by the Lyapunov stability theorem employs a carefully constructed virtual mechanical quantity P to ensure the system convergence.The virtual mechanical quantity P is chosen by two approaches according to the forms of limit set,where P = —pf is suitable for regular limit set and a new different P is constructed for irregular one.The proposed tracking control theory is demonstrated on a four-level quantum system by means of numerical simulation experiments.

Dynamical properties of a kind of SIR model with constant vaccination rate and impulsive state feedback control

Considering the fact that the production and provision of some vaccines are ordered and governed by the government according to the history data of disease, a kind of SIR model with constant vaccination rate and impulsive state feedback control is presented. The dynamical properties of semi-continuous three-dimensional SIR system can be obtained by discussing the properties of the corresponding two-dimensional system in the limit set. The existence and uniqueness of order-1 periodic solution are discussed by using the successive function and the compression mapping theorem. A new theorem for the orbital stability of order-1 periodic solution is proved by geometric method. Finally, numerical simulations are given to verify the mathematical results and some conclusions are given. The results show that the disease can be controlled to a lower level by means of impulsive state feedback control strategy, but cannot be eradicated.

SEMIGROUP APPROACH TO A DOUBLY DEGENERATE PARABOLIC EQUATION

Basing on the L1-type estimates, we present a semigroup approach to the initial valueproblem for a doubly nonlinear degenerate parabolic equation, arising from some physical back-grounds. The relation between the corresponding limit set and equilibrium set is also discussed.