Stability of an $$\varvec{}{}$$th root functional equation in $$\varvec{C}^{*}$$C∗-algebras: a fixed point approach

In this paper, we introduce an \(m{\text{th}}\) root functional equation. Using the fixed point approach, we prove the Hyers–Ulam stability of the \(m{\text{th}}\) root functional equation in \(C^{*}\)-algebras.     

Charge-transfer complex formation between p-chloranil and 1,n-dicarbazolylalkanes

Dimer model compounds of polyvinylcarbazoles (1,n-di(N-carbazolyl)alkanes, when n=1-5) were synthesized to model the effects of distance and orientation between carbazole groups in polymeric systems. Charge-transfer (CT) complexes of carbazole, N-ethylcarbazole and 1,n-di(N-carbazolyl)alkanes with p-chloranil (p-CHL) have been investigated spectrophotometrically in dichloromethane. The colored products are measured spectrophotometrically at different wavelength depending on the electronic transition between donors and acceptor. The formation constants of the CT complexes were determined by the Benesi-Hildebrand equation. The thermodynamic parameters were calculated by Van't Hoff equation. Stochiometries of the complexes formed between donors and acceptor were defined by the Job's method of the continuous variation and found in 1:1 complexation with donor and acceptor at the maximum absorption bands.     

Metal-Templated Design of Chemically Switchable Protein Assemblies with High-Affinity Coordination Sites

To mimic a hypothetical pathway for protein evolution, we previously tailored a monomeric protein (cyt cb₅₆₂) for metal-mediated self-assembly, followed by re-design of the resulting oligomers for enhanced stability and metal-based functions. We show that a single hydrophobic mutation on the cyt cb₅₆₂ surface drastically alters the outcome of metal-directed oligomerization to yield a new trimeric architecture, (TriCyt1)_3. This nascent trimer was redesigned into second and third-generation variants (TriCyt2)₃ and (TriCyt3)₃ with increased structural stability and preorganization for metal coordination. The three TriCyt variants combined furnish a unique platform to 1) provide tunable coupling between protein quaternary structure and metal coordination, 2) enable the construction of metal/pH-switchable protein oligomerization motifs, and 3) generate a robust metal coordination site that can coordinate all mid-to-late first-row transition-metal ions with high affinity.     

Vranceanu surface in $$ \mathbb{E}^4 $$ with pointwise 1- type Gauss map

In this article we investigate Vranceanu rotation surfaces with pointwise 1- type Gauss map in Euclidean 4-space $ \mathbb{E}^4 $ \mathbb{E}^4 . We show that a Vranceanu rotation surface M has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficent conditions for Vranceanu rotation surface to have pointwise 1-type Gauss map.     

Templated construction of a Zn-selective protein dimerization motif

Here, we report that the approach of metal-templated ligand synthesis can be applied to construct a dimeric protein assembly ((BMOE)RIDC1(2)), which is stabilized by noncovalent interactions and flexible covalent cross-linkers around the Zn templates. Despite its flexibility, (BMOE)RIDC1(2) selectively binds Zn(II) over other divalent metals and undergoes dimerization upon metal binding. Such simultaneous fulfillment of plasticity and selectivity is a hallmark of cellular signaling events that involve ligand/metal-induced protein dimerization.     

Lower limits of detection in speciation analysis by coupling high-performance liquid chromatography and chemical-vapor generation

Speciation studies are much more important than total element determination because toxicity of many elements depends on their chemical forms. Nobody can claim that a foodstuff is very dangerous to eat by determining total arsenic due to the possibility that the arsenic could be present in non-toxic forms. Hence, speciation studies are crucial in any matrix relevant to human beings.Trace-element speciation requires sufficiently sensitive procedures to monitor each species at trace levels. One way to increase the sensitivity for elements forming volatile species is coupling high-performance liquid chromatography (HPLC) with chemical-vapor generation (CVG). This review aims to highlight not only development of HPLC-CVG techniques for ultratrace-elemental speciation in a variety of matrices but also their application. In addition, we discuss the advantages and the disadvantages of these techniques.     

Aflatoxin species: their health effects and determination methods in different foodstuffs

Carcinogenic and mutagenic properties of aflatoxin species are known in literature. Their intake over a long time period might be health-dangerous for human even at trace levels. It is well known that different foodstuffs can be contaminated by aflatoxin species through growing and storage. Due to the serious health effects, sensitive determination of aflatoxin species in any matrices related with the human being is very crucial at trace levels. In literature, there are sensitive techniques to analyze the different samples for the contents of their aflatoxin species. Each technique has some advantages and disadvantages over the other techniques. This review aims to summarize the different health effects of aflatoxin species, development of analytical techniques and applications of developed techniques in a variety of matrices.      

Conformational analysis and vibrational spectroscopic investigation of 3-phenylpropylamine

The possible stable forms of 3-phenylpropylamine (3-PPA) molecule were experimentally and theoretically studied by infrared and Raman spectroscopy. FT-IR and Raman spectra of 3-PPA were recorded in the regions of 4000–400 cm⁻¹ and 3700–60 cm⁻¹, respectively. The potential energy surface corresponding to the internal rotations of the molecule was investigated by semi-empirical quantum mechanical methods, and appropriate conformers defined with B3LYP hybrid density functional theory method along with the basis sets of different size and type. Results from experimental and theoretical data showed the trans–trans–gauche (TTG) to be the most stable form of a 3-PPA molecule.     

Dynamic analysis and synchronization control of an unusual chaotic system with exponential term and coexisting attractors

This paper reports a new four-dimensional chaotic system consisting of an exponential nonlinear term, two quadratic nonlinear terms and five linear terms. The system has only one equilibrium and performs stability, periodicity and chaos with the variation of the parameters. It losses its stability with the occurrence of Hopf bifurcation and goes into chaos via period-doubling bifurcation. One more interesting feature of the system is that it can generate multiple coexisting attractors for different initial conditions, such as two strange attractors with one limit cycle, one strange attractor with two limit cycles, etc. The dynamic properties of the system are presented by numerical simulation includes bifurcation diagrams, Lyapunov exponent spectrum and phase portraits. An electronic circuit is constructed to implement the chaotic attractor of the system. Based on the linear quadratic regulator (LQR) method, the synchronization control of the system is investigated.