A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples.

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13] studied the difference sequence spaces ∞（A）, c（A）, and co（A）. Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces e0^r, ec^r, and e∞^r, respectively. The main purpose of this article is to introduce the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））consisting of all sequences whose mth order differences are in the Euler spaces e0^r, ec^r, and e∞^r, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces e0^r△^（m））, ec^r△^（m））, and e∞^r△^（m））, and the Schauder basis of the spaces e0^r△^（m））, ec^r△^（m））. The last section of the article is devoted to the characterization of some matrix mappings on the sequence space ec^r△^（m））.

ON THE m^(th) ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS

In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.

MiR-96-5p inhibition induces cell apoptosis in gastric adenocarcinoma

BACKGROUND Gastric adenocarcinoma(GAC)mortality rates have remained relatively changed over the past 30 years,and it continues to be one of the leading causes of cancerrelated death.AIM To search for novel miRNAs related to GAC prognosis and further investigate the effect of miR-96-5p on MGC-803 cells.METHODS The miRNA expression profile data of GAC based on The Cancer Genome Atlas were obtained and used to screen differently expressed miRNAs(DEMs)and DEMs related to GAC prognosis.Then,the expression of DEMs related to GAC prognosis was identified in GAC tumor samples and adjacent normal samples by qRT-PCR.The target gene,ZDHHC5,of miR-96-5p was predicted using TargetScan,miRTarBase,and miRDB databases and confirmed by luciferase reporter assay.Furthermore,MGC-803 cells were transfected with inhibitor NC,miR-96-5p inhibitor,si-ZDHHC5,or miR-96-5p inhibitor+si-ZDHHC5,and then cell apoptosis was detected by flow cytometry.The expression of ZDHHC5,Bcl-2,and COX-2 was detected using western blotting.RESULTS A total of 299 DEMs and 35 DEMs related to GAC prognosis were screened based on The Cancer Genome Atlas.Then compared with adjacent normal samples,the levels of miR-96-5p,miR-222-5p,and miR-652-5p were remarkably increased,while miR-125-5p,miR-145-3p,and miR-379-3p levels were reduced in GAC tumor samples(P<0.01),which were consistent with bioinformatics analysis.Furthermore,ZDHHC5 was defined as a direct target gene of miR-96-5p.miR-96-5p inhibition increased the number of apoptotic cells as well as promoted the expression of ZDHHC5,Bcl-2,and COX-2 in MGC-803 cells(P<0.01).After ZDHHC5 inhibition,the number of apoptotic cells and the expression of ZDHHC5,Bcl-2,and COX-2 were reduced.The addition of an miR-96-5p inhibitor partly reversed these effects(P<0.01).CONCLUSION Our findings identified six miRNAs related to GAC prognosis and suggested that downregulated miR-96-5p might induce cell apoptosis via upregulating ZDHHC5 expression in MGC-803 cells.

Three-dimensional hydrodynamic model of Xiamen waters

A semi-implicit and Eulerian - Lagrangian finite difference method for three-dimensionalshallow flow has been extended to a more complete system of equations incorporating second-moment turbulence closure model and transport equations of salinity and temperature. The simulation for flooding and drying of mudflats has been improved. The model is applied to Xiamen waters. Based on extensive survey data, water level elevation, temperature and salinity field along the eastern open boundary and at the Jiulong River inlets and runoffs are analyzed, specified and calibrated. The computed results show good agreement with the measured data, reproduce flooding, emergence of large and complex mudflat region.

A Three-dimensional Forecasting Model for Oil Spill

A 3-D forecasting model for oil-spill is developed using the finite difference method to numerically solve the shallow water equation. The instantaneous flow distribution in the studied area is calculated and the trajectory of the oil-slick centroid is predicted by means of Lagrange’s method. The computed results agree with the observed data well, this shows that this 3-D forecasting model has high accuracy.

Sex-Dependent Glial Signaling in Pathological Pain:Distinct Roles of Spinal Microglia and Astrocytes

Increasing evidence suggests that spinal micro- glia regulate pathological pain in males. In this study, we investigated the effects of several microglial and astroglial modulators on inflammatory and neuropathic pain follow- ing intrathecal injection in male and female mice. These modulators were the microglial inhibitors minocycline and ZVEID （a caspase-6 inhibitor） and the astroglial inhibitors L-α-aminoadipate （L-AA, an astroglial toxin） and car- benoxolone （a connexin 43 inhibitor）, as well as U0126 （an ERK kinase inhibitor） and D-JNKI-1 （a c-Jun N-terminal kinase inhibitor）. We found that spinal administration of minocycline or ZVEID, or Caspase6 deletion, reduced formalin-induced inflammatory and nerve injury-induced neuropathic pain primarily in male mice. In contrast, intrathecal L-AA reduced neuropathic pain but not inflam- matory pain in both sexes. Intrathecal U0126 and D-JNKI- 1 reduced neuropathic pain in both sexes. Nerve injury caused spinal upregulation of the astroglial markers GFAP and Connexin 43 in both sexes. Collectively, our data confirmed male-dominant microglial signaling but also revealed sex-independent astroglial signaling in the spinal cord in inflammatory and neuropathic pain.