Exploration of some indole-based hydroxamic acids as histone deacetylase inhibitors and antitumor agents

In our search for novel small molecules targeting histone deacetylases, we have designed and synthesized a series of novel hydroxamic acids incorporating indole moiety as a cap group (3a–l). Biological evaluation showed that these hydroxamic acids potently inhibited HDAC2 with IC₅₀ values in submicromolar range and up to tenfold (compound 3j) better than that of SAHA (also known as suberoylanilide hydroxamic acid). In four human cancer cell lines [SW620 (colon), PC-3 (prostate), AsPC-1 (pancreatic), NCI-H23 (lung)], the synthesized compounds that exhibited potent cytotoxicity with several compounds (3k, 3l) were found to be 12- to 77-fold more cytotoxic than SAHA. Docking experiments indicated that the compounds tightly bound to HDAC2 at the active binding site with binding affinities much higher than that of SAHA. Our present results demonstrate that these novel hydroxamic acids are potential for further development as anticancer agents.     

Mössbauer Studies of Core-Shell FeO/Fe3O4 Nanoparticles

Physics of the Solid State - FeO/Fe3O4 nanoparticles were synthesized by thermal decomposition. Electron microscopy revealed that these nanoparticles were of the core-shell type and had a spherical...     

Thermoelastic Stress Analysis of Structures Under Natural Vibrations

The paper focuses on stress analyses of structures subjected to excitation forces operating at resonant frequencies. The structures are analysed experimentally using the Thermoelastic Stress Analysis (TSA) technique. Experiments are carried out for fixed-free beams of different dimensions and materials, and also for a steel rectangular plate with clamped edges. These structures are excited by a shaker via a stinger. For materials with low thermal conductivity, the agreement between the theory, numerical results and experimental results is excellent. As the thermal conductivity of the material is increased, the correspondence is not as close. This is because of non-adiabatic behaviour. The implications of these results are discussed in detail in the paper and a means of deriving the severity of heat transfer is provided. Other factors that influence the TSA results from structures under natural loading are also discussed.     

Blow-Up Rate Estimates and Liouville Type Theorems for a Semilinear Heat Equation with Weighted Source

We study the Liouville-type theorem for the semilinear parabolic equation \(u_t-\Delta u =|x|^a u^p\) with \(p>1\) and \(a\in {\mathbb R}\). Relying on the recent result of Quittner (Math Ann, doi: 10.1007/s00208-015-1219-7, 2015), we establish the optimal Liouville-type theorem in dimension \(N=2\), in the class of nonnegative bounded solutions. We also provide a partial result in dimension \(N\ge 3\). As applications of Liouville-type theorems, we derive the blow-up rate estimates for the corresponding Cauchy problem.     

Versions of Ekeland’s variational principle involving set perturbations

We consider Ekeland’s variational principle for multivalued maps. Instead of dealing with directional perturbations in a direction of the positive cone of the image space, we perturb the map under question by a convex subset of the positive cone to get stronger and more general versions. Many example are provided to highlight relations of our results to existing ones, including their advantages.     

Decision with Dempster-Shafer belief functions: Decision under ignorance and sequential consistency

This paper examines proposals for decision making with Dempster-Shafer belief functions from the perspectives of requirements for rational decision under ignorance and sequential consistency. The focus is on the proposals by Jaffray & Wakker and Giang & Shenoy applied for partially consonant belief functions. We formalize the concept of sequential consistency of an evaluation model and prove results about sequential consistency of Jaffray-Wakker’s model and Giang-Shenoy’s model under various conditions. We demonstrate that the often neglected assumption about two-stage resolution of uncertainty used in Jaffray-Wakker’s model actually disambiguates the foci of a belief function, and therefore, makes it a partially consonant on the extended state space.     

Normal form for the symmetry-breaking bifurcation in the nonlinear Schrödinger equation

We derive and justify a normal form reduction of the nonlinear Schrödinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential. We prove persistence of normal form dynamics for both supercritical and subcritical pitchfork bifurcations in the time-dependent solutions of the nonlinear Schrödinger equation over long but finite time intervals.