On Jensen's functional equation

Summary Letf be a map from a groupG into an abelian groupH satisfyingf(xy) + f(xy ^–1) = 2f(x), f(e) = 0, wherex, y G ande is the identity inG. A set of necessary and sufficient conditions forS(G, H) = Hom(G, H) is given whenG is abelian, whereS(G, H) denotes all the solutions of the functional equation. The case whenG is non-abelian is also discussed.     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

New necessary conditions on the existence of abelian difference sets

In this paper we develop a new method to obtain identities in a group algebraGF(p)G if an abelian difference set of ordern0 (modp) exists inG. We give an explicit formula ifp ² orp ³ is the exactp-power dividingn. This generalizes the approach of Wilbrink, Arasu and the author. The proof presented here uses some knowledge about field extensions of thep-adic numbers.     

Bootstrap,wild bootstrap,and asymptotic normality

Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle     

Some properties of the riesz charge associated with a δ-subharmonic function

The first property is a refinement of earlier results of Ch. de la Vallée Poussin, M. Brelot, and A. F. Grishin. Let w=u–v with u, v superharmonic on a suitable harmonic space (for example an open subset of R ⁿ ), and let [w]=[u]–[v] denote the associated Riesz charge. If w0, and if E denotes the set of those points of at which the lim inf of w in thefine topology is 0, then the restriction of [w] to E is 0. Another property states that, if e denotes a polar subset of such that the fine lim inf of |w| at each point of e is finite, then the restriction of [w] to e is 0.     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Quantitative and Qualitative Analysis of the Anti-Proliferative Potential of the Pyrazole Scaffold in the Design of Anticancer Agents

The current work presents an objective overview of the impact of one important heterocyclic structure, the pyrazole ring, in the development of anti-proliferative drugs. A set of 1551 pyrazole derivatives were extracted from the National Cancer Institute (NCI) database, together with their growth inhibition effects (GI%) on the NCI’s panel of 60 cancer cell lines. The structures of these derivatives were analyzed based on the compounds’ averages of GI% values across NCI-60 cell lines and the averages of the values for the outlier cells. The distribution and the architecture of the Bemis–Murcko skeletons were analyzed, highlighting the impact of certain scaffold structures on the anti-proliferative effect’s potency and selectivity. The drug-likeness, chemical reactivity and promiscuity risks of the compounds were predicted using AMDETlab. The pyrazole ring proved to be a versatile scaffold for the design of anticancer drugs if properly substituted and if connected with other cyclic structures. The 1,3-diphenyl-pyrazole emerged as a useful scaffold for potent and targeted anticancer candidates.     

N-Butyrylated Hyaluronic Acid Achieves Anti-Inflammatory Effects In Vitro and in Adjuvant-Induced Immune Activation in Rats

Previously synthesized N-butyrylated hyaluronic acid (BHA) provides anti-inflammatory effects in rat models of acute gouty arthritis and hyperuricemia. However, the mechanism of action remains to be elucidated. Herein, the anti-inflammatory and antioxidative activities of BHA and the targeted signaling pathways were explored with LPS-induced RAW264.7 and an adjuvant-induced inflammation in a rat model. Results indicated that BHA inhibited the generation of pro-inflammatory cytokines TNFα, IL-1β and IL-6, reduced ROS production and down-regulated JAK1-STAT1/3 signaling pathways in LPS-induced RAW264.7. In vivo, BHA alleviated paw and joint swelling, decreased inflammatory cell infiltration in paw tissues, suppressed gene expressions of p38 and p65, down-regulated the NF-κB and MAPK signaling pathways and reduced protein levels of TNFα, IL-1β and IL-6 in joint tissues of arthritis rats. This study demonstrated the pivotal role of BHA in anti-inflammation and anti-oxidation, suggesting the potential clinical value of BHA in the prevention of inflammatory arthritis and is worthy for development as a new pharmacological treatment.     

Anti-Inflammatory Effects of Spiramycin in LPS-Activated RAW 264.7 Macrophages

Drug repurposing is a simple concept with a long history, and is a paradigm shift that can significantly reduce the costs and accelerate the process of bringing a new small-molecule drug into clinical practice. We attempted to uncover a new application of spiramycin, an old medication that was classically prescribed for toxoplasmosis and various other soft-tissue infections; specifically, we initiated a study on the anti-inflammatory capacity of spiramycin. For this purpose, we used murine macrophage RAW 264.7 as a model for this experiment and investigated the anti-inflammatory effects of spiramycin by inhibiting the production of pro-inflammatory mediators and cytokines. In the present study, we demonstrated that spiramycin significantly decreased nitric oxide (NO), interleukin (IL)-1β, and IL-6 levels in lipopolysaccharide (LPS)-stimulated RAW 264.7 cells. Spiramycin also inhibited the expression of NO synthase (iNOS), potentially explaining the spiramycin-induced decrease in NO production. In addition, spiramycin inhibited the phosphorylation of mitogen-activated protein kinases (MAPKs); extracellular signal-regulated kinase (ERK) and c-Jun N terminal kinase (JNK) as well as the inactivation and subsequent nuclear translocation of nuclear factor κB (NF-κB). This indicated that spiramycin attenuates macrophages’ secretion of IL-6, IL-1β, and NO, inducing iNOS expression via the inhibition of the NF-κB and MAPK signaling pathways. Finally, we tested the potential application of spiramycin as a topical material by human skin primary irritation tests. It was performed on the normal skin (upper back) of 31 volunteers to determine whether 100 μM and μM of spiramycin had irritation or sensitization potential. In these assays, spiramycin did not induce any adverse reactions. In conclusion, our results demonstrate that spiramycin can effectively attenuate the activation of macrophages, suggesting that spiramycin could be a potential candidate for drug repositioning as a topical anti-inflammatory agent.