Design,Synthesis, and Biological Evaluation of Desmuramyl Dipeptides Modified by Adamantyl-1,2,3-triazole

Muramyl dipeptide (MDP) is the smallest peptidoglycan fragment able to trigger the immune response. Structural modification of MDP can lead to the preparation of analogs with improved immunostimulant properties, including desmuramyl peptides (DMPs). The aim of this work was to prepare the desmuramyl peptide (L-Ala-D-Glu)-containing adamantyl-triazole moiety and its mannosylated derivative in order to study their immunomodulatory activities in vivo. The adjuvant activity of the prepared compounds was evaluated in a murine model using ovalbumin as an antigen, and compared to the reference adjuvant ManAdDMP. The results showed that the introduction of the lipophilic adamantyl-triazole moiety at the C-terminus of L-Ala-D-Glu contributes to the immunostimulant activity of DMP, and that mannosylation of DMP modified with adamantyl-triazole causes the amplification of its immunostimulant activity.     

Advantages,sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem

Central European Journal of Operations Research - In the paper we consider advantages, sensitivity and application efficiency of the new method for solving multi-objective linear fractional...     

Improved Heinz inequalities via the Jensen functional

By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.     

On meromorphic extendibility

Let D be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint real-analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for poles of a meromorphic extension of f through D and thus reduce the question of meromorphic extendibility to the question of holomorphic extendibility. Let A(D) be the algebra of all continuous functions on which are holomorphic on D. We prove that a continuous function f on bD extends meromorphically through D if and only if there is an N∈N∪{0} such that the change of argument of Pf+Q along bD is bounded below by −2πN for all P,Q∈A(D) such that Pf+Q≠0 on bD. If this is the case then the meromorphic extension of f has at most N poles in D, counting multiplicity.     

On refined Hardy-type inequalities with fractional integrals and fractional derivatives

The aim of this paper is to present new more general Hardy-type inequalities for different kinds of fractional integrals and fractional derivatives.     

Levinson’s Type Generalization of the Edmundson–Lah–Ribarič Inequality

Mediterranean Journal of Mathematics - In this paper the authors give a brief historical remark on Edmundson–Madansky and Lah–Ribarič inequalities, which are both special cases of...     

Extension of Hilbert's inequality

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.     

On some general Hilbert’s inequalities with non-conjugate parameters

A generalized discrete Hilbert’s and Hardy-Hilbert’s inequality with non-conjugate parameters can be established by means of Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our results with some previously known from the literature. We also obtain the improvements on some earlier results.