Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces

In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists $v$ a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces $ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}$. Moreover, we show the asymptotic behavior of the global solution $v$. i.e., $\|v(t)\|_{ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}}$ decays to zero as time goes to infinity.     

Compound A Increases Cell Infiltration in Target Organs of Acute Graft-versus-Host Disease (aGVHD) in a Mouse Model

Systemic steroids are used to treat acute graft-versus-host disease (aGVHD) caused by allogenic bone marrow transplantation (allo-BMT); however, their prolonged use results in complications. Hence, new agents for treating aGVHD are required. Recently, a new compound A (CpdA), with anti-inflammatory activity and reduced side effects compared to steroids, has been identified. Here, we aimed to determine whether CpdA can improve the outcome of aGVHD when administered after transplantation in a mouse model (C57BL/6 in B6D2F1). After conditioning with 9Gy total body irradiation, mice were infused with bone marrow (BM) cells and splenocytes from either syngeneic (B6D2F1) or allogeneic (C57BL/6) donors. The animals were subsequently treated (3 days/week) with 7.5 mg/kg CpdA from day +15 to day +28; the controls received 0.9% NaCl. Thereafter, the incidence and severity of aGVHD in aGVHD target organs were analyzed. Survival and clinical scores did not differ significantly; however, CpdA-treated animals showed high cell infiltration in the target organs. In bulk mixed lymphocyte reactions, CpdA treatment reduced the cell proliferation and expression of inflammatory cytokines and chemokines compared to controls, whereas levels of TNF, IL-23, chemokines, and chemokine receptors increased. CpdA significantly reduced proliferation in vitro but increased T cell infiltration in target organs.     

Crystal chemistry of three new monodimensional fluorometalates templated with ethylenediamine

Three new monodimensional hybrid metal (Ti, In, Al) fluorides are synthesized with ethylenediamine (en) as a templating agent in solvothermal conditions assisted by microwave heating. All structures involve inorganic chains built up from TiO₂F₄ octahedra connected by two opposite O²⁻ vertices in [H₂en]·(TiOF₄) (I), from InF₆(H₂O) pentagonal bipyramids linked by F–F edges in [H₂en]·(InF₄(H₂O))₂·H₂O (II) and from (Al₇F₃₀)⁹⁻ polyanions sharing two opposite AlF₆ octahedra in [H₂en]₃·(Al₆F₂₄) (III). I is tetragonal, P4/ncc, a = 12.761(3) Å, c = 8.041(3) Å; II is orthorhombic, F2dd, a = 6.904(5) Å, b = 16.559(5) Å, c = 19.777(4) Å and III is monoclinic, P2₁/n, a = 9.387(2) Å, b = 6.710(2) Å, c = 21.513(6) Å, β = 97.18(3)°.     

Photooxidation of acyclovir with thermally generated triplet excited ketones. A comparison with type I and II photosensitizers

The antiviral drug acyclovir (Ac, 1) was treated with triplet excited ketones, which have been generated in thermal decomposition of 3-(hydroxymethyl)-3,4,4-trimethyl-1,2-dioxetane (HTMD), in the dark. Three major oxidation products were detected by means of spectroscopic measurements. The products were (2-hydroxyethoxy) methyl spiroiminodihydantoin (2), (2-hydroxyethoxy) methyl (amino)-2-imino-1,2-dihydroimidazole-5-one (3), and 2,2-diamino-4-[(2-hydroxyethoxy) methyl) amino)-5-[2H]-oxazolone (4). Equal amounts of type I and type II photooxidation products were found, as could be established by comparison with predominant type I (riboflavin) and type II (rose bengal) photosensitizers. The concentration and time profiles for the HTMD-induced oxidation of Ac were also determined. The participation of singlet oxygen in HTMD-induced oxidation was confirmed by the substantial D(2)O effect in the formation of spiroiminodihydantoin (2).     

On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z^″=λz, where λ is a function in C^∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition

     

Around Jensen’s inequality for strongly convex functions

In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve the Hölder-McCarthy inequality under suitable conditions. More precisely we show that if \(Sp\left( A \right) \subset \left( 1,\infty \right) \), then

$$\begin{aligned} {{\left\langle Ax,x \right\rangle }^{r}}\le \left\langle {{A}^{r}}x,x \right\rangle -\frac{{{r}^{2}}-r}{2}\left( \left\langle {{A}^{2}}x,x \right\rangle -{{\left\langle Ax,x \right\rangle }^{2}} \right) ,\quad r\ge 2 \end{aligned}$$

and if \(Sp\left( A \right) \subset \left( 0,1 \right) \), then

$$\begin{aligned} \left\langle {{A}^{r}}x,x \right\rangle \le {{\left\langle Ax,x \right\rangle }^{r}}+\frac{r-{{r}^{2}}}{2}\left( {{\left\langle Ax,x \right\rangle }^{2}}-\left\langle {{A}^{2}}x,x \right\rangle \right) ,\quad 0<r<1 \end{aligned}$$

for each positive operator A and \(x\in \mathcal {H}\) with \(\left\| x \right\| =1\).

     

An algorithm for the estimation of a regression function by continuous piecewise linear functions

The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L ₂ risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.     

Bayesian modeling of forestry data with R using optimization and simulation tools

Data generated in forestry biometrics are not normal in statistical sense as they rarely follow the normal regression model. Hence, there is a need to develop models and methods in forest biometric applications for non-normal models. Due to generality of Bayesian methods it can be implemented in the situations when Gaussian regression models do not fit the data. Data on diameter at breast height (dbh), which is a very important characteristic in forestry has been fitted to Weibull and gamma models in Bayesian paradigm and comparisons have also been made with its classical counterpart. It may be noted that MCMC simulation tools are used in this study. An attempt has been made to apply Bayesian simulation tools using \textbf{R} software.     

Synthesis of Cholesterol-Conjugated Magnetic Nanoparticles for Purification of Human Paraoxonase 1

Human serum paraoxonase 1 (PON1) is known as an antioxidant and is also involved in the detoxification of many compounds. In this study, a novel purification strategy was employed to purify the PON1 by using cholesterol-conjugated magnetic nanoparticles. Magnetic nanoparticles were synthesized and conjugated with cholesterol through diazotized p-aminohippuric acid. In Fourier transform infrared spectrum of cholesterol-p-aminohippuric acid-Fe₃O₄ nanoparticles, the appearance of peaks at 3,358.3, 1,645 cm⁻¹, and at 2,334.9 cm⁻¹ confirmed the conjugation. The molecular weight of purified PON1 was nearly 45 kDa on sodium dodecyl sulfate (SDS)–polyacrylamide gel electrophoresis (PAGE), and isoelectric point was 5.3. The specific activity was 438 U mg⁻¹ protein, and the purification fold was 515 with 73% yield. The K _m values were 1.3 and 0.74 mM with paraoxon and phenyl acetate, respectively. Western blot of 2D-PAGE confirmed the homogeneity and stability of the enzyme. Mg⁺², Mn⁺², glycerol, (NH₄)₂SO₄, PEG 6000, Triton X-100, and phenylmethylsulfonyl fluoride did not show any effect on activity. Pb⁺², Co⁺², Zn²⁺, ethanol, β-mercaptoethanol, and acetone reduced the activity while Ni²⁺, Cd²⁺, Cu²⁺, iodoacetic acid, SDS, dimethylformamide, DMSO inhibited the activity. In vitro enzyme activity was slightly reduced by acetyl salicylic and acetaminophen and reduced 50% with amino glycosides and ampicillin antibiotics at concentrations of 0.6 and 30 mg ml⁻¹, respectively. This is the first report for the synthesis of cholesterol-conjugated magnetic nanoparticles for simple purification of PON1 enzyme.     

New ceramides from Platytaenia multicaule

Phytochemical investigation of Platytaenia multicaule resulted in the isolation of two new ceramides, N-triacontylpentadecanamide and 1,3,4-trihydroxy-2,dodecanoylamino-(24E)-unacotenene, along with two known compounds, beta-sitosterol and beta-sitosterol glycoside. The structure elucidation of the isolated compounds was based primarily on 1D and 2D NMR analyses, including COSY, NOESY, HMQC, and HMBC correlations.