On the directed Full Degree Spanning Tree problem

We study the parameterized complexity of a directed analog of the Full Degree Spanning Tree problem where, given a digraph $D$ and a nonnegative integer $k$, the goal is to construct a spanning out-tree $T$ of $D$ such that at least $k$ vertices in $T$ have the same out-degree as in $D$. We show that this problem is W[1]-hard even on the class of directed acyclic graphs. In the dual version, called Reduced Degree Spanning Tree, one is required to construct a spanning out-tree $T$ such that at most $k$ vertices in $T$ have out-degrees that are different from that in $D$. We show that this problem is fixed-parameter tractable and that it admits a problem kernel with at most $8k$ vertices on strongly connected digraphs and $O\left(k^2\right)$ vertices on general digraphs. We also give an algorithm for this problem on general digraphs with running time $O(5.942^k?n^{O\left(1\right)})$, where $n$ is the number of vertices in the input digraph.     

Projective synchronization between different fractional‐order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique

In the present article, the authors have proposed a modified projective adaptive synchronization technique for fractional‐order chaotic systems. The adaptive projective synchronization controller and identification parameters law are developed on the basis of Lyapunov direct stability theory. The proposed method is successfully applied for the projective synchronization between fractional‐order hyperchaotic Lü system as drive system and fractional‐order hyperchaotic Lorenz chaotic system as response system. A comparison between the effects on synchronization time due to the presence of fractional‐order time derivatives for modified projective synchronization method and proposed modified adaptive projective synchronization technique is the key feature of the present article. Numerical simulation results, which are carried out using Adams–Boshforth–Moulton method show that the proposed technique is effective, convenient and also faster for projective synchronization of fractional‐order nonlinear dynamical systems. Copyright © 2013 John Wiley & Sons, Ltd.     

Kaluza-Klein reduction and consistency of the massive spin-3/2 theory with external interaction

A gauge-invariant Rarita-Schwinger theory of a massive spin-3/2 particle interacting with external electromagnetic, gravitational and dilaton fields is obtained by Kaluza-Klein reduction of a massless Rarita-Schwinger theory with graviational interaction. Fermionic gauge invariance serves to determine the background equations of motion. The couplings with external fields obtained by the Kaluza-Klein reduction are shown to lead to the absence of the classical Velo-Zwanziger problem and on quantizing using Dirac's procedure, the field anticommutators are found to be positive definite.     

CP violation at colliders

The prospects of experimental detection ofCP violation ate ⁺ e ^? and\(pp/p\bar p\) colliders are reviewed. After a general discussion on the quantities which can measureCP violation and on the implications of theCPT theorem, various possibilities of measuringCP violation arising outside the standard model are taken up.CP violation in leptonic processes, especially polarization effects ine ⁺ e ^?→l ⁺ l ^? are discussed next.CP violation in\(t\overline t \) andW ⁺ W ^? production and decay is also described.     

One pot synthesis of α,β-epoxy ketones by oxidative coupling of methyl arenes with cinnamic acids involving C(sp3)―H activation and decarboxylative strategy

A new one pot oxidative coupling of methyl arenes with cinnamic acids has been developed for the synthesis of α,β-epoxy ketones using MnO₂/TBHP combination. The process involves a co-existing C(sp³)―H activation and decarboxylation under aqueous medium, which makes it practical and attractive.     

Studies on Mo doped vanadium oxide film by pulsed RF magnetron sputtering

Molybdenum doped vanadium oxide film on quartz and silicon substrates are grown by pulsed RF magnetron sputtering method. Surface morphology, phase analysis and oxide states are investigated by field emission scanning electron microscopy, X‐ray diffraction and X‐ray photoelectron spectroscopy techniques, respectively. Crystalline nature of the film deposited on both quartz and silicon are depicted. The transmittance and reflectance spectra recorded for the entire solar region. Further, optical constants viz. optical band gap and refractive index of the deposited films are estimated. Wavelength dependent low reflectance characteristic is observed for the deposited film on silicon. IR emittance (ε_IR) and sheet resistance (R_s) of the film are also evaluated. Copyright © 2017 John Wiley & Sons, Ltd.     

Statistical optimization of conditions for protease production fromBacillus sp. and its scale-up in a bioreactor

A statistical approach, response surface methodology (RSM), was used to study the production of extracellular protease fromBacillus sp., which has properties of immense industrial importance. The most influential parameters for protease production obtained through the method of testing the parameters one at a time were starch, soybean meal, CaCl₂, agitation rate, and inoculum density. This method resulted in the production of 2543 U/mL of protease in 48 h fromBacillus sp. Based on these results, face-centered central composite design falling under RSM was employed to further enhance protease activity. The interactive effect of the most influential parameters resulted in a 1.50-fold increase in protease production, yielding 3746 U/mL in 48 h. Analysis of variance showed the adequacy of the model and verification experiments confirmed its validity. On subsequent scale-up in a 30-L bioreactor using conditions optimized through RSM, 3978 U/mL of protease was produced in 18 h. This clearly indicated that the model remained valid even on a large scale. RSM is a quick process for optimization of a large number of variables and provides profound insight into the interactive effect of various parameters involved in protease production.     

Role of Magnetic Exchange Interactions in the Magnetization Relaxation of {3d–4f} Single‐Molecule Magnets: A Theoretical Perspective

Combined density functional and ab initio calculations are performed on two isomorphous tetranuclear {Ni₃^IIILn^III} star‐type complexes [Ln=Gd ( 1 ), Dy ( 2 )] to shed light on the mechanism of magnetic exchange in 1 and the origin of the slow magnetization relaxation in complex 2 . DFT calculations correctly reproduce the sign and magnitude of the J values compared to the experiments for complex 1 . Acute ?Ni?O?Gd bond angles present in 1 instigate a significant interaction between the 4f_xyz orbital of the Gd^III ion and 3d orbital of the Ni^II ions, leading to rare and strong antiferromagnetic Ni???Gd interactions. Calculations reveal the presence of a strong next‐nearest‐neighbour Ni???Ni antiferromagnetic interaction in complex 1 leading to spin frustration behavior. CASSCF+RASSI‐SO calculations performed on complex 2 suggest that the octahedral environment around the Dy^III ion is neither strong enough to stabilize the m_J |±15/2〉 as the ground state nor able to achieve a large ground‐state–first‐excited‐state gap. The ground‐state Kramers doublet for the Dy^III ion is found to be the m_J |±13/2〉 state with a significant transverse anisotropy, leading to very strong quantum tunneling of magnetization (QTM). Using the POLY_ANISO program, we have extracted the J_NiDy interaction as ?1.45 cm^?1. The strong Ni???Dy and next‐nearest‐neighbour Ni???Ni interactions are found to quench the QTM to a certain extent, resulting in zero‐field SMM behavior for complex 2 . The absence of any ac signals at zero field for the structurally similar [Dy(AlMe₄)₃] highlights the importance of both the Ni???Dy and the Ni???Ni interactions in the magnetization relaxation of complex 2 . To the best of our knowledge, this is the first time that the roles of both the Ni???Dy and Ni???Ni interactions in magnetization relaxation of a {3d–4f} molecular magnet have been established.     

Alkaloidal Phytoconstituents for Diabetes Management: Exploring the Unrevealed Potential

The main characteristic feature of diabetes mellitus is the disturbance of carbohydrate, lipid, and protein metabolism, which results in insulin insufficiency and can also lead to insulin resistance. Both the acute and chronic diabetic cases are increasing at an exponential rate, which is also flagged by the World Health Organization (WHO) and the International Diabetes Federation (IDF). Treatment of diabetes mellitus with synthetic drugs often fails to provide desired results and limits its use to symptomatic treatment only. This has resulted in the exploration of alternative medicine, of which herbal treatment is gaining popularity these days. Owing to their safety benefits, treatment compliance, and ability to exhibit effects without disturbing internal homeostasis, research in the field of herbal and ayurvedic treatments has gained importance. Medicinal phytoconstituents include micronutrients, amino acids, proteins, mucilage, critical oils, triterpenoids, saponins, carotenoids, alkaloids, flavonoids, phenolic acids, tannins, and coumarins, which play a dynamic function in the prevention and treatment of diabetes mellitus. Alkaloids found in medicinal plants represent an intriguing potential for the inception of novel approaches to diabetes mellitus therapies. Thus, this review article highlights detailed information on alkaloidal phytoconstituents, which includes sources and structures of alkaloids along with the associated mechanism involved in the management of diabetes mellitus. From the available literature and data presented, it can be concluded that these compounds hold tremendous potential for use as monotherapies or in combination with current treatments, which can result in the development of better efficacy and safety profiles.