Stable Large-Scale Perturbations in Interacting Dark-Energy Model

It is found that the evolutions of density perturbations on the super-Hubble scales are unstable in the model with dark-sector interaction $Q$ proportional to the energy density of cold dark matter (CDM) $\rho_m$ and constant equation of state parameter of dark energy $w_d$. In this paper, to avoid the instabilities, we suggest a new covariant model for the energy-momentum transfer between DE and CDM. Then we show that the the large-scale instabilities of curvature perturbations can be avoided in our model in the universe filled only by DE and CDM. Furthermore, by including the additional components of radiation and baryons, we calculate the dominant non-adiabatic modes in the radiation era and find that the modes grow in the power law with exponent at the order of unit.Comment: 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1110.180

New Interaction between Dark Energy and Dark Matter Changes Sign during Cosmological Evolution

It is found by Cai and Su that the interaction between dark energy and cold dark matter is likely to change the sign during the cosmological evolution. Motivated by this, we suggest a new form of interaction between dark energy and dark matter, which changes from negative to positive as the expansion of our universe changes from decelerated to accelerated. We find that the interacting model is consistent with the second law of thermodynamics and the observational constraints. And, we also discuss the unified adiabatic-squared sound speed of the model.Comment: 16 pages, 3 figure, 1 table. Final version in PR

Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales

AbstractLet T be a time scale such that 0,T∈T, β,γ⩾0 and 0<η<ρ(T). We consider the following p-Laplacian three-point boundary problem on time scales(φp(uΔ(t)))∇+λh(t)f(u(t))=0,t∈(0,T),u(0)−βuΔ(0)=γuΔ(η),uΔ(T)=0, where p>1, λ>0, h∈Cld((0,T),[0,∞)) and f∈C([0,∞),(0,∞)). Some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. In doing so the usual restriction that f0=limu→0+f(u)φp(u) and f∞=limu→∞f(u)φp(u) exist is removed. An example is also given to illustrate the main results

Marsupialization facilitates movement of the cystic lesion-associated deeply impacted mandibular third molar in spite of its mature roots

Background: The odontogenic cystic lesions happened in the angle and ramus region are frequently associated with impacted mandibular third molars. The treatment plan was difficult to work out for the huge cystic lesions with deeply impacted third molars, since the enucleation with simultaneously removing the deeply impacted teeth may cause serious complications. Therefore, the marsupialization of the cystic lesions followed by enucleation with tooth removal has also been advocated. The aim of this study was to explore the movement of cystic lesion-associated deeply impacted mandibular third molars (IMTM) after marsupialization. Material and Methods: Between July 2009 and December 2015, patients who had mandibular cystic lesion associated with IMTM and underwent marsupialization followed by enucleation with tooth extraction were included in our retrospective study. The clinical and pathological data was collected. The distance and direction of movement of the IMTM after marsupialization was measured on panoramic radiograph and computed tomography. Results: Four male and six female patients whose ages ranged from 14 years to 67 years were enrolled in this study. Among the all impacted molars, there were 3 cases with mature roots. After marsupialization, all the cystic lesions shrunk and all impacted teeth moved toward the bony windows, and the distance of tooth movement were from 8.3mm to 12.1mm. The complications included swelling and pain, while no numbness of the ipsilateral lower lip was happened. Conclusions: Marsupialization can promote the movement of impacted teeth with or without mature roots, and may be an optimal treatment approach for the huge posterior mandibular cystic lesions with deeply impacted third molar. Key words:Mandibular cystic lesion, impacted third mandibular molar, marsupialization, mature root

Tricin protects rats from ovariectomized-induced osteoporosis by enhancing Wnt/β-catenin pathway

Purpose: To investigate the effects of tricin on ovariectomized-induced osteoporosis, and unravel theunderling mechanism of action.Methods: An osteoporosis rat model was established by conducting ovariectomy (OVX). Changes in the microstructure of the trabecular bone were visualized using Hematoxylin and eosin (H&amp;E) staining, and a three-point bending test was employed to assess the biomechanical stability of the femurs, after the administration of tricin (20 and 40 mg/kg). Subsequently, bone marrow mesenchymal stem cells (BMSCs) were isolated and treated with tricin (7 and 15 μM). Alizarin red staining was performed to assess mineralization, and Runt-related transcription factor 2 (RUNX2); osteocalcin (OCN) and collagen type I alpha 1 (Col1a1) were quantified using western blot analysis. The Wnt/β-catenin pathway related proteins, i.e., Wnt3a, β-catenin, glycogen synthase kinase-3 β (GSK-3 β) were determined.Results: Ovariectomy induced thinner and discontinuous trabecular bone, with increased marrow cavities, while application of tricin significantly improved the density and regularity meshwork, but reduced marrow cavities. Tricin also enhanced biomechanical competence as seen in the upregulated maximum load, stiffness, young modulus and maximum stress compared with OVX group (p &lt; 0.01). Furthermore, tricin increased calcification in BMSCs, and significantly upregulated the expressions of RUNX2, OCN and COL1A1 when compared with OVX group (p &lt; 0.01). It promoted Wnt/β-catenin signaling by enhancing Wnt3a and β-catenin, while inhibiting GSK3β expression, compared with OVX group (p &lt; 0.05 or p &lt; 0.01).Conclusion: Tricin exerts protective effects against OVX-induced osteoporosis by enhancing Wnt/β-catenin pathway. Thus, tricin is a potential therapeutic agent for the management of osteoporosis

Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem

We firstly prove that β-times integrated α-resolvent operator function ((α,β)-ROF) satisfies a functional equation which extends that of β-times integrated semigroup and α-resolvent operator function. Secondly, for the inhomogeneous α-Cauchy problem cDtαu(t)=Au(t)+f(t), t∈(0,T), u(0)=x0, u'(0)=x1, if A is the generator of an (α,β)-ROF, we give the relation between the function v(t)=Sα,β(t)x0+(g1*Sα,β)(t)x1+(gα-1*Sα,β*f)(t) and mild solution and classical solution of it. Finally, for the problem cDtαv(t)=Av(t)+gβ+1(t)x, t>0, v(k)(0)=0, k=0,1,…,N-1, where A is a linear closed operator. We show that A generates an exponentially bounded (α,β)-ROF on a Banach space X if and only if the problem has a unique exponentially bounded classical solution vx and Avx∈L loc 1(ℝ+,X). Our results extend and generalize some related results in the literature