A uniqueness result related to certain non-linear differential polynomials sharing the same 1-points

We prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share two or three sets which will improve some existing results.     

Simulation model for shapiro time delay and light deflection experiments

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.     

Synthesis of a boronated amino acid as a potential neutron therapy agent: 1-amino-3-[(dihydroxyboryl)ethyl]cyclobutanecarboxylic acid

A novel boronated aminocyclobutanecarboxylic acid was synthesized in 10 steps for potential use in neutron capture therapy. The molecule was modeled after the unnatural amino acid 1-aminocyclobutanecarboxylic acid, which has shown high uptake in brain tumors.     

Mean-field theories of spin glasses

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.     

Probing CPT violation in neutrino oscillation: A three flavor analysis

We have studied CPT violation in neutrino oscillation considering three flavor framework with matter effect. We have constructed a new way to find the oscillation probability incorporating CPT violating terms without any approximation. Then CPT   violation with atmospheric neutrinos for a magnetized iron calorimeter detector considering the muons (directly measurable with high resolution) of the charge current events has been studied for zero and nonzero θ₁₃${\theta }_{13}$ values. It is found that a potential bound of δb₃₂?6×¹⁰⁻²⁴ GeV$\delta b_{32}?6\times {10}^{-24}\text{GeV}$ at 99% CL can be obtained with 1 Mton.year exposure of this detector; and unlike neutrino beam experiments, there is no possibility to generate ‘fake’ CPT violation due to matter effect with atmospheric neutrinos. The advantages of atmospheric neutrinos to discriminate CPT violation from CP violation and nonstandard interactions are also discussed.     

Hadron mass spectrum from lattice QCD

Finite temperature lattice simulations of quantum chromodynamics (QCD) are sensitive to the hadronic mass spectrum for temperatures below the "critical" temperature T(c) ≈ 160 MeV. We show that a recent precision determination of the QCD trace anomaly shows evidence for the existence of a large number of hadron states beyond those known from experiment. The lattice results are well represented by an exponentially growing mass spectrum up to a temperature T=155 MeV. Using simple parametrizations of the hadron mass spectrum we show how one may estimate the total spectral weight in these yet undermined states.     

Camouflaging Structural Diversity: Co‐crystallization of Two Different Nanoparticles Having Different Cores But the Same Shell

Two ligand‐protected nanoscale silver moieties, [Ag₄₆(SPhMe₂)₂₄(PPh₃)₈](NO₃)₂ and [Ag₄₀(SPhMe₂)₂₄(PPh₃)₈](NO₃)₂ (abbreviated as Ag₄₆ and Ag₄₀, respectively) with almost the same shell but different cores were synthesized simultaneously. As their external structures are identical, the clusters were not distinguishable and become co‐crystallized. The occupancy of each cluster was 50 %. The outer shell of both is composed of Ag₃₂S₂₄P₈, which is reminiscent of fullerenes, and it encapsulates a well‐studied core, Ag₁₄ and a completely new core, Ag₈, which correspond to a face‐centered cube and a simple cube, respectively, resulting in the Ag₄₆ and Ag₄₀ clusters. The presence of two entities (Ag₄₀ and Ag₄₆ clusters) in a single crystal and their molecular formulae were confirmed by detailed electrospray ionization mass spectrometry. The optical spectrum of the mixture showed unique features which were in good agreement with the results from time‐dependent density functional theory (TD‐DFT).     

Role of recycling in improving the performance of chromatographic solvent gradient purifications

With significant advancement in the upstream processing technology, downstream processing of large bio-molecules is becoming the bottle-neck in the production chain. To face this challenge, design and development of efficient separation processes has become crucial. As a step towards boosting the performance of a chromatographic separation process through improved design, we investigated the potential of recycling as a process option. The most important advantage of recycling is that it can be implemented in an existing batch system without any major investment and consultation. Although impure products are recycled in industries, it is done as additional batch, and only then, when the recoverable product is valuable enough to surpass the loss of productivity in running the additional batches. In our study, on the other hand, it was found that a well-designed recycle can not only improve the yield, but also the productivity of a multi-component purification. A series of multiobjective optimization studies were carried out on multi-component separation to comprehend the role of recycling with reference to an industrially relevant problem, i.e. the chromatographic purification step of the production process of calcitonin.