Higher Order Efficiency,Saddle Point Optimality,and Duality for Vector Optimization Problems

In this paper, we intend to characterize the strict local efficient solution of order m for a vector minimization problem in terms of the vector saddle point. A new notion of strict local saddle point of higher order of the vector-valued Lagrangian function is introduced. The relationship between strict local saddle point and strict local efficient solution is derived. Lagrange duality is formulated, and duality results are presented.     

Nanolayered multilayer coatings of CrN/CrAlN prepared by reactive DC magnetron sputtering

Single-phase CrN and CrAlN coatings were deposited on silicon and mild steel substrates using a reactive DC magnetron sputtering system. The structural characterization of the coatings was done using X-ray diffraction (XRD). The XRD data showed that both the CrN and CrAlN coatings exhibited B1 NaCl structure with a prominent reflection along (2 0 0) plane. The bonding structure of the coatings was characterized by X-ray photoelectron spectroscopy and the surface morphology of the coatings was studied using atomic force microscopy. Subsequently, nanolayered CrN/CrAlN multilayer coatings with a total thickness of approximately 1 μm were deposited on silicon substrates at different modulation wavelengths (Λ). The XRD data showed that all the multilayer coatings were textured along {2 0 0}. The CrN/CrAlN multilayer coatings exhibited a maximum nanoindentation hardness of 3125 kg/mm² at a modulation wavelength of 72 Å, whereas single layer CrN and CrAlN deposited under similar conditions exhibited hardness values of 2375 and 2800 kg/mm², respectively. Structural changes as a result of heating of the multilayer coatings in air (400-800 °C) were characterized using XRD and micro-Raman spectroscopy. The XRD data showed that the multilayer coatings were stable up to a temperature of 650 °C and peaks pertaining to Cr₂O₃ started appearing at 700 °C. These results were confirmed by micro-Raman spectroscopy. Nanoindentation measurements performed on the heat-treated coatings revealed that the multilayer coatings retained hardness as high as 2250 kg/mm² after annealing up to a temperature of 600 °C.     

Sorption of radioactive strontium on a silica-titania mixed hydrous oxide gel

A silica-titania (Si–Ti) mixed hydroxide gel with Ti to Si mole ratio of 11 was prepared. Studies on the sorption of radiostrontium from alkaline solutions having various concentrations of sodium were carried out with Si–Ti. The distribution coefficient (K _d) of strontium decreased with increasing concentrations of sodium from 0.1 to 4.0 mol·dm^–3. The plot of logK _d versus log [Na⁺] gave a slope of –0.55 as against the theoretical value of –2.0. This suggests that some other paths in addition to the simple stoichiometric ion exchange is also existing for sorption. From pH titrations the pH_pzc of Si–Ti was found to be 4.22 coinciding nearly with the pH sorption edge. An attempt was made to correlate the sorption results with the surface characteristics of the sorbent. It was found that sorption is favored when the surface of the sorbent transforms into an anionic form. Sharp increase in the sorption of strontium was observed when the equilibrium pH was between 7 and 10. This behavior could be attributed to the abrupt increase in net negative charge on the surface of the sorbent.     

Spontaneous symmetry breaking in a time-dependent space-time

Spontaneous symmetry breaking of a ⁴ quantum of field theory in a time-dependent space-time, de Sitter space, is discussed in the Schrödinger picture. Instead of the usual cutoff method we use an-regularization procedure to deal with the divergent integrals.     

A Rare Low‐Spin CoIV Bis(β‐silyldiamide) with High Thermal Stability: Steric Enforcement of a Doublet Configuration

Attempted preparation of a chelated Co^II β‐silylamide resulted in the unprecedented disproportionation to Co⁰ and a spirocyclic cobalt(IV) bis(β‐silyldiamide): [Co[(N^tBu)₂SiMe₂]₂] ( 1 ). Compound 1 exhibited a room‐temperature magnetic moment of 1.8 B.M. and a solid‐state axial EPR spectrum diagnostic of a rare S= configuration for tetrahedral Co^IV. Ab initio semicanonical coupled‐cluster calculations (DLPNO‐CCSD(T)) revealed the doublet state was clearly preferred (?27 kcal mol^?1) over higher spin configurations only for the bulky tert‐butyl‐substituted analogue. Unlike other Co^IV complexes, 1 had remarkable thermal stability, and was demonstrated to form a stable self‐limiting monolayer in preliminary atomic layer deposition (ALD) surface saturation experiments. The ease of synthesis and high stability make 1 an attractive starting point to investigate otherwise inaccessible Co^IV intermediates and for synthesizing new materials.     

Preparation, characterization, and surface modification of silver nanoparticles in formamide

The reduction of silver ions in formamide is shown to take place spontaneously at room temperature without addition of any reductant. The growth of Ag particles was found to be dependent on Ag+ ion concentration. In the absence of any stabilizer, deposition of silver film on the glass walls of the container takes place. However, in the presence of poly(N-vinyl-2-pyrrolidone) (PVP) or colloidal silica (SiO2), which are capable of stabilizing silver nanoparticles by complexing and providing support, a clear dispersion was obtained. The formation of the silver nanoparticles under different conditions was investigated through UV-visible absorption spectrophotometry, gas chromatography, and also electron and atomic force microscopic techniques. Atomic force microscopy results for silver films prepared in the absence of any stabilizer showed the formation of polygonal particles with sizes around 100 nm. Transmission electron microscopy results showed that the prepared silver particles in the presence of PVP were around 20 nm. The Ag nanoparticles get oxidized in the presence of chloroform and toluene. Surface modification of silver film was done in the presence of the tetrasodium salt of ethylenediaminetetraaceticacid (Na4EDTA). It was shown that the reactivity of the silver film increased in its presence. The Fermi potential of silver particles in the presence of Na4EDTA seems to lie between -0.33 and -0.446 V vs NHE.     

Conversion of 4-amino-4H-1,2,4-triazole to 1,3-bis(1H-azol-l-yl)-2-aryl-2-propanols and 1-phenacyl-4-[(benzoyl or 4-toluenesulfonyl)-imino]-(1H-1,2,4-triazolium) Ylides

A series of 1,3-bis(1H-azol-1-yl)-2-aryl-2-propanols 17 were synthesized in an one-pot procedure by reacting l-aryl-2-(1H-1,2,4-triazol-l-yl)- or l-aryl-2-(1H-imidazol-l-yl)ethanones with dimethylsulfoxonium methide in the presence of either 1,2,4-triazole or imidazole. The aromatic groups in 17 were either 4-bromo-, 4-chloro-, 2,4-dichloro- or 2,4-difluorophenyl. 4-Amino-4H-1,2,4-triazole was acylated with either benzoyl or 4-toluene-sulfonyl chloride to afford [4-(benzoyl or 4-toluenesulfonyl)amino]4H-1,2,4-triazole. Subsequent alkylations with 4-bromo- or 4-chlorophenacyl bromide produced 1-(4-bromo- or 4-chlorophenacyl)-4-[(benzoyl- or 4-toluenesulfonyl)amino]-1H-1,2,4-triazolium bromides. Neutralizations of these salts provided the corresponding ylides.     

Optical sensor for the visual detection of mercury using mesoporous silica anchoring porphyrin moiety

A low cost, solid optical sensor for the rapid detection of low concentrations of Hg2+ in aqueous media was prepared by the monolayer functionalization of mesoporous silica with 5,10,15,20-tetraphenylporphinetetrasulfonic acid (TPPS), anchored by N-trimethoxysilylpropyl-N,N,N-trimethylammonium chloride (TMAC). The detection is based on the color change of TPPS from orange to green as a result of the formation of a charge-transfer complex with Hg2+. The intensity of the charge-transfer band varies linearly with Hg2+ in the concentration range from zero to 2.5 x 10(-7) mol dm(-3). The lower detection limit observed for Hg2+ concentration is 1.75 x 10(-8) mol dm(-3). The material exhibits good chemical and mechanical stability, and did not show any degradation of TPPS for a period of eight months. The sensor was applied for the analysis of various environmental samples. The effects of pH, sample volume, reaction time, amount of material, and the presence of foreign ions on the detection method are discussed.     

Iterative Arylation of Amino Acids and Aliphatic Amines via δ‐C(sp3)−H Activation: Experimental and Computational Exploration

Directed C?H functionalization has been realized as a complementary tool to the traditional approaches for a straightforward access of non‐proteinogenic amino acids; albeit such a process is restricted mostly up to the γ‐position. In the present work, we demonstrate the diverse (hetero)arylation of amino acids and analogous aliphatic amines selectively at the remote δ‐position by tuning the reactivity controlled by ligands. An organopalladium δ‐C(sp³)?H activated intermediate has been isolated and crystallographically characterized. Mechanistic investigations carried out experimentally in conjunction with computational studies shed light on the difference in the mechanistic picture depending on the substrate structure.     

Ligand‐Enabled PdII‐Catalyzed Iterative γ‐C(sp3)−H Arylation of Free Aliphatic Acid

C?H functionalization of aliphatic carboxylic acids without attaching exogenous auxiliary has been so far limited at the proximal β‐position. In this work, we demonstrate a ligand enabled palladium catalyzed first regioselective distal γ‐C(sp3)?H functionalization of aliphatic carboxylic acids without incorporating an exogenous directing group. Aryl iodides containing versatile functional groups including complex organic molecules are well tolerated with good to excellent yields during the γ‐C(sp3)?H arylation reaction. Interestingly, weak coordination of carboxylate group can be further extended for sequential hetero di‐arylation. Application of the protocol has been showcased by synthesizing substituted α‐tetralone. Mechanistic investigations have been carried out to shed light on the reaction pathway.