Stability of nonlinear AR‐GARCH models

Abstract. This article studies the stability of nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a nonlinear autoregression of order p [AR(p)] with the conditional variance specified as a nonlinear first‐order generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. Conditions under which the model is stable in the sense that its Markov chain representation is geometrically ergodic are provided. This implies the existence of an initial distribution such that the process is strictly stationary and β‐mixing. Conditions under which the stationary distribution has finite moments are also given. The results cover several nonlinear specifications recently proposed for both the conditional mean and conditional variance, and only require mild moment conditions.     

Multi‐Enzymatic Synthesis of Optically Pure β‐Hydroxy α‐Amino Acids

A novel enzymatic production system of optically pure β‐hydroxy α‐amino acids was developed. Two enzymes were used for the system: an N‐succinyl L ‐amino acid β‐hydroxylase (SadA) belonging to the iron(II)/α‐ketoglutarate‐dependent dioxygenase superfamily and an N‐succinyl L ‐amino acid desuccinylase (LasA). The genes encoding the two enzymes are part of a gene set responsible for the biosynthesis of peptidyl compounds found in the Burkholderia ambifaria AMMD genome. SadA stereoselectively hydroxylated several N‐succinyl aliphatic L ‐amino acids and produced N‐succinyl β‐hydroxy L ‐amino acids, such as N‐succinyl‐L ‐β‐hydroxyvaline, N‐succinyl‐L ‐threonine, (2S,3R)‐N‐succinyl‐L ‐β‐hydroxyisoleucine, and N‐succinyl‐L ‐threo‐β‐hydroxyleucine. LasA catalyzed the desuccinylation of various N‐succinyl‐L ‐amino acids. Surprisingly, LasA is the first amide bond‐forming enzyme belonging to the amidohydrolase superfamily, and has succinylation activity towards the amino group of L ‐leucine. By combining SadA and LasA in a preparative scale production using N‐succinyl‐L ‐leucine as substrate, 2.3 mmol of L ‐threo‐β‐hydroxyleucine were successfully produced with 93% conversion and over 99% of diastereomeric excess. Consequently, the new production system described in this study has advantages in optical purity and reaction efficiency for application in the mass production of several β‐hydroxy α‐amino acids.

     

Highly Enantioselective Phase‐Transfer Catalytic α‐Alkylation of α‐tert‐Butoxycarbonyllactams: Construction of β‐Quaternary Chiral Pyrrolidine and Piperidine Systems

A new enantioselective α‐alkylation of α‐tert‐butoxycarbonyllactams for the construction of β‐quaternary chiral pyrrolidine and piperidine core systems is reported. α‐Alkylations of N‐methyl‐α‐tert‐butoxycarbonylbutyrolactam and N‐diphenylmethyl‐α‐tert‐butoxycarbonylvalerolactam under phase‐transfer catalytic conditions (solid potassium hydroxide, toluene, −40 °C) in the presence of (S,S)‐3,4,5‐trifluorophenyl‐3,3′,5,5′‐tetrahydro‐2,6‐bis(3,4,5‐trifluorophenyl)‐4,4′‐spirobi[4H‐dinaphth[2,1‐c:1′,2′‐e]azepinium] bromide [(S,S)‐NAS Br] (5 mol%) afforded the corresponding α‐alkyl‐α‐tert‐butoxycarbonyllactams in very high chemical (up to 99%) and optical yields (up to 98% ee). Our new catalytic systems provide attractive synthetic methods for pyrrolidine‐ and piperidine‐based alkaloids and chiral intermediates with β‐quaternary carbon centers.     

Searching for health beneficial n‐3 and n‐6 fatty acids in plant seeds

Various plant seeds have received little attention in fatty acid research. Seeds from 30 species mainly of Boraginaceae and Primulaceae were analysed in order to identify potential new sources of the n‐3 PUFA α‐linolenic acid (ALA) and stearidonic acid (SDA) and of the n‐6 PUFA γ‐linolenic acid (GLA). The fatty acid distribution differed enormously between genera of the same family. Echium species (Boraginaceae) contained the highest amount of total n‐3 PUFA (47.1%), predominantly ALA (36.6%) and SDA (10.5%) combined with high GLA (10.2%). Further species of Boraginaceae rich in both SDA and GLA were Omphalodes linifolia (8.4, 17.2%, resp.), Cerinthe minor (7.5, 9.9%, resp.) and Buglossoides purpureocaerulea (6.1, 16.6%, resp.). Alkanna species belonging to Boraginaceae had comparable amounts of ALA (37.3%) and GLA (11.4%) like Echium but lower SDA contents (3.7%). Different genera of Primulaceae (Dodecatheon and Primula) had varying ALA (14.8, 28.8%, resp.) and GLA portions (4.1, 1.5%, resp.), but similar amounts of SDA (4.9, 4.5%, resp.). Cannabis sativa cultivars (Cannabaceae) were rich in linoleic acid (57.1%), but poor in SDA and GLA (0.8, 2.7%, resp.). In conclusion, several of the presented plant seeds contain considerable amounts of n‐3 PUFA and GLA, which could be relevant for nutritional purposes due to their biological function as precursors for eicosanoid synthesis. Practical applications: N‐3 PUFA are important for human health and nutrition. Unfortunately, due to the increasing world population, overfishing of the seas and generally low amounts of n‐3 PUFA in major oil crops, there is a demand for new sources of n‐3 PUFA. One approach involves searching for potential vegetable sources of n‐3 PUFA; especially those rich in ALA and SDA. The conversion of ALA to SDA in humans is dependent on the rate‐limiting Δ6‐desaturation. Plant‐derived SDA is therefore a promising precursor regarding the endogenous synthesis of n‐3 long‐chain PUFA in humans. The present study shows that, in addition to seed oil of Echium, other species of Boraginaceae (Cerinthe, Omphalodes, Lithospermum, Buglossoides) and Primulaceae (Dodecatheon, Primula), generally high in n‐3 PUFA (30–50%), contain considerable amounts of SDA (5–10%). Therefore, these seed oils could be important for nutrition.     

Synthesis of ω‐amino‐α‐phenylcarbonate alkanes and their polymerization to [n]‐polyurethanes

Aliphatic [n]‐polyurethanes have recently been synthesized from ω‐isocyanato‐α‐alkanols or, more traditionally, by cationic ring‐opening polymerization of cyclourethanes or by the Bu₂Sn(OMe)₂‐promoted polycondensation of ω‐hydroxy‐α‐O‐phenylurethane alkanes. For the latter procedures, the conditions employed do not seem to be suitable for highly functionalized monomers. In contrast, the polymerization of ω‐amino‐α‐phenylcarbonate alkanes is expected to occur under milder conditions. ω‐Amino‐α‐phenylcarbonate alkanes have been synthesized from 6‐aminohexanol (1) and 3‐aminopropanol (6). The procedure involves the N‐Boc protection of the amino group, followed by activation of the alcohol. Removal of the N‐Boc affords the corresponding ω‐amino‐1‐O‐phenyloxycarbonyloxyalkane hydrochlorides. Other oligomeric comonomers between 1 and 6 have been prepared. The polymerization of these precursors takes place in the absence of metal catalysts to afford the corresponding linear and regioregular [n]‐polyurethanes. The procedure described is useful for the preparation of stable ω‐amino‐α‐phenylcarbonate alkane derivatives, which possess varied chain lengths between the terminal functions. These monomers yield [n]‐polyurethanes having various structures starting from just two aminoalkanols. The polyurethanes were obtained in high yields, with reasonable molecular weight and polydispersity values, and they were characterized spectroscopically and thermally. These studies reveal constitutionally uniform structures that are free of carbonate or urea linkages. Copyright © 2010 Society of Chemical Industry     

Turbulent forward–reverse mixing characteristics in vessel with multiple‐turbine impellers

BACKGROUND: Mixing in unbaffled vessel with multiple‐turbine impellers was studied. The mixing time and mixing power were evaluated in relation to the distance between impellers and the number of impellers. RESULTS: It has been confirmed that frequency of oscillation has no influence on the mixing time and mixing power values or on drag and added mass coefficients. The coefficients were greater when distance between impellers was smaller. Moreover added mass coefficient was dependent on Reynolds number (n_i > 2). Compared with unidirectional mixing conditions, for systems with one type of impeller, the power requirement was about 38% higher for forward‐reverse mixing. Despite the fact that the power demand was greater, the mixing time was not shorter, but about 30% higher than unidirectional mixing in a baffled vessel. However, the forward‐reverse mixing mode exhibits a higher level of homogeneity which it achieved faster than unidirectional mixing. CONCLUSION: The power requirements and mixing time for forward‐reverse mixing mode were higher in comparison with unidirectional mixing. Despite this, higher values of homogeneity were achieved faster. Higher levels of shear rate and better homogeneity indicate that forward‐reverse mixing can be beneficial for multi‐phase mixing in vessels with multiple impellers. © 2012 Society of Chemical Industry     

Enantioselective α‐Alkylation of Benzylideneamino tert‐Butyl Malonates by Phase‐Transfer Catalysis

A new enantioselective synthetic method for the synthesis of α,α‐dialkylmalonates with a quaternary carbon center was developed via α‐alkylation of prochiral malonates by phase‐transfer catalysis (PTC). Asymmetric α‐alkylation of benzylideneamino tert‐butyl α‐methylmalonates under phase‐transfer catalytic conditions in the presence of (S,S)‐3,4,5‐trifluorophenyl‐NAS bromide afforded the corresponding α,α‐dialkylmalonates in high yields (up to 97%) with excellent enantioselectivities (up to 98% ee). The products were then selectively hydrolyzed to chiral malonic monoacids under basic, acidic, or catalytic hydrogenation conditions.

     

Catalytic Hydrogenation of α‐Iminophosphonates as a Method for the Synthesis of Racemic and Optically Active α‐Aminophosphonates

It was shown that the catalytic hydrogenation of α‐iminophosphonates by molecular hydrogen can serve as a convenient method for the synthesis of racemic and optically active α‐aminophosphonates. Up to 94% ee was achieved in the rhodium‐catalyzed enantioselective hydrogenation using chiral ligand (R)‐BINAP.     

Asymptotic self‐similarity and wavelet estimation for long‐range dependent fractional autoregressive integrated moving average time series with stable innovations

Abstract. Methods for parameter estimation in the presence of long‐range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long‐range dependence in the case of heavy‐tailed distributions. In this paper, we focus on the estimation of the Hurst parameter H = d + 1/α for long‐range dependent FARIMA time series with symmetric α‐stable (1 < α < 2) innovations. We establish the consistency and the asymptotic normality of two types of wavelet estimators of the parameter H. We do so by exploiting the fact that the integrated series is asymptotically self‐similar with parameter H. When the parameter α is known, we also obtain consistent and asymptotically normal estimators for the fractional differencing exponent d = H ? 1/α. Our results hold for a larger class of causal linear processes with stable symmetric innovations. As the wavelet‐based estimation method used here is semi‐parametric, it allows for a more robust treatment of long‐range dependent data than parametric methods.     

Bio‐Based Hybrid Magnetic Latex Particles Containing Encapsulated γ ‐Fe2O3 by Miniemulsion Copolymerization of Soybean Oil‐Acrylated Methyl Ester and Styrene

This work reports the use of acrylated fatty acid methyl ester (AFAME) as a biomonomer for the synthesis of bio‐based hybrid magnetic particles poly(styrene‐co‐AFAME)/γ‐Fe₂O₃ produced by miniemulsion polymerization. Poly(styrene‐co‐AFAME)/γ‐Fe₂O₃ can be tailored for use in various fields by varying the content of AFAME. The strategy employed is to encapsulate superparamagnetic iron oxide nanoparticles (SPIONs) as γ‐Fe₂O₃ into a styrene/AFAME‐based copolymer matrix. Raman spectroscopy is employed to ensure the formation of the SPIONs (γ‐Fe₂O₃) obtained by a co‐precipitation technique followed by oxidation of Fe₃O₄. The functionalization of SPIONs with oleic acid (OA) is carried out to increase the SPIONs–monomer affinity. The presence of OA on the surface of γ‐Fe₂O₃ is certified by identification of main absorption bands by fourier‐transform infrared spectroscopy (FTIR). Thermal analysis (differential thermogravimetry/differential thermo analysis and differential scanning calorimetry) results of poly(styrene‐co‐AFAME)/γ‐Fe₂O₃ show an increase in AFAME content leading to a lower copolymer glass transition temperature (T _g). Dynamic light scattering (DLS) measurements result in poly(styrene‐co‐AFAME)/γ‐Fe₂O₃ particles with diameter in the range of 100–150 nm. It is also observed by transmission electron microscopy (TEM) and cryo‐TEM techniques that γ‐Fe₂O₃ particles are successfully encapsulated into the poly(styrene‐co‐AFAME) matrix.     

Evidence of Strict Stereospecificity in the Structure of sn‐1,2‐Diacyl‐3‐Acetyl‐Glycerols from Euonymus maximowiczianus Seeds Using Nuclear Magnetic Resonance Spectroscopy

Asymmetric, optically active sn‐1,2‐diacyl‐3‐acetyl‐glycerols (AcDAG) have been known to scientists for several decades. However, to date, the problem of their structure has not been definitely resolved, which has led to a vast diversity of terms used for their designation in the literature. Using two‐dimensional nuclear magnetic resonance, we have investigated AcDAG from the mature seeds of Euonymus maximowiczianus, from which we have been able to both identify a correlation of the methyl group in acetic acid residue with protons at the carbon atom at sn‐3 position in the glycerol residue of the AcDAG molecule and, for the first time, demonstrate that this correlation is observed exclusively with one carbon atom at the α‐position, but not with two as would have been expected in case of a racemic mixture. Moreover, results of our analysis of AcDAG isolated from the seeds of E. maximowiczianus directly confirm that diacylglycerol‐3‐acetyl‐transferase is responsible for their biosynthesis, which reveals a strict specificity not only to acetyl‐CoA as one of the substrates but also to the sn‐3‐position of the glycerol residue in sn‐1,2‐diacylglycerol during their biosynthesis.     

(R)‐α‐Lipoyl‐Glycyl‐L‐Prolyl‐L‐Glutamyl Dimethyl Ester Codrug as a Multifunctional Agent with Potential Neuroprotective Activities

The (R)‐α‐lipoyl‐glycyl‐L ‐prolyl‐L ‐glutamyl dimethyl ester codrug (LA‐GPE, 1 ) was synthesized as a new multifunctional drug candidate with antioxidant and neuroprotective properties for the treatment of neurodegenerative diseases. Physicochemical properties, chemical and enzymatic stabilities were evaluated, along with the capacity of LA‐GPE to penetrate the blood–brain barrier (BBB) according to an in vitro parallel artificial membrane permeability assay for the BBB. We also investigated the potential effectiveness of LA‐GPE against the cytotoxicity induced by 6‐hydroxydopamine (6‐OHDA) and H₂O₂ on the human neuroblastoma cell line SH‐SY5Y by using the 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide (MTT) reduction assay. Our results show that codrug 1 is stable at both pH 1.3 and 7.4, exhibits good lipophilicity (log P=1.51) and a pH‐dependent permeability profile. Furthermore, LA‐GPE was demonstrated to be significantly neuroprotective and to act as an antioxidant against H₂O₂‐ and 6‐OHDA‐induced neurotoxicity in SH‐SY5Y cells.     

Preparation and properties of organosoluble,colorless, and high‐pretilt‐angle polyimides based on an alicyclic dianhydride and long‐main‐chain alkyl‐group‐containing diamines

Alicyclic polyimides (PIs) were prepared from 3‐carboxylmethyl‐cyclopentane‐1,2,4‐tricarboxylic acid dianhydride and α,ω‐di(4‐aminophenoxyl)alkanes. These PIs possessed good solubility in aprotic, strongly polar solvents such as N‐methyl‐2‐pyrrolidone, N,N‐dimethylacetamide, N,N‐dimethyl formamide, and m‐cresol. They possessed high transparency in visible wavelengths and were almost colorless. The pretilt angle of a liquid‐crystal display with these PIs as the alignment layer increased linearly as the length of the alkyloxy groups increased; it was close to 5° for the PI samples PI‐10 and PI‐12. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 2814–2820, 2001     

Chemical Synthesis of the Epimeric (23R)‐ and (23S)‐Fluoro Derivatives of Bile Acids via Horner–Wadsworth–Emmons Reaction

A method for the synthesis of two (23R)‐ and (23S)‐epimeric pairs of 23‐fluoro‐3α,7α,12α‐trihydroxy‐5β‐cholan‐24‐oic acid and 23‐fluoro‐3α,7α‐dihydroxy‐5β‐cholan‐24‐oic acid is described. The key intermediates, 23,24‐dinor‐22‐aldehyde peracetates were prepared from cholic and chenodeoxycholic acids via the 24‐nor‐22‐ene, 24‐nor‐22ξ,23‐epoxy, and 23,24‐dinor‐22‐aldehyde derivatives. The Horner–Wadsworth–Emmons reaction of the 23,24‐dinor‐22‐aldehydes using triethyl 2‐fluoro‐2‐phosphonoacetate in the presence of LiCl and 1,8‐diazabicyclo[5,4,0]undec‐7‐ene (DBU), and subsequent hydrogenation of the resulting 23ξ‐fluoro‐22‐ene ethyl esters, followed by hydrolysis, gave a mixture of the epimeric (23R)‐ and (23S)‐fluorinated bile acids which were resolved efficiently by preparative RP‐HPLC. The stereochemical configuration of the fluorine atom at C‐23 in the newly synthesized compounds was confirmed directly by the X‐ray crystallographic data. The ¹H and ¹³C NMR spectral differences between the (23R)‐ and (23S)‐epimers were also discussed.     

Homogeneous graft copolymerization of chitosan with butyl acrylate by γ‐irradiation via a 6‐O‐maleoyl‐N‐phthaloyl‐chitosan intermediate

The graft copolymerization of butyl acrylate (BA) onto chitosan was tried via a new protection‐graft‐deprotection procedure. About 6‐O‐maleoyl‐N‐phthaloyl‐chitosan was synthesized and characterized by Fourier transform infrared spectra analysis (FT‐IR) and ¹H‐NMR. Because the intermediate 6‐O‐maleoyl‐N‐phthaloyl‐chitosan was soluble in organic solvents, the graft copolymerization was carried out in a homogeneous system. Grafting was initiated by γ‐irradiation. The graft extent was dependent on the irradiation dose and the concentration of BA monomer, and copolymers with grafting above 100% were readily prepared. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 489–493, 2006     

Asymmetric Aza‐Morita–Baylis–Hillman‐Type Reactions: The Highly Enantioselective Reaction between Unmodified α,β‐ Unsaturated Aldehydes and N‐Acylimines by Organo‐co‐catalysis

The highly enantioselective organo‐co‐catalytic aza‐Morita–Baylis–Hillman (MBH)‐type reaction between N‐carbamate‐protected imines and α,β‐unsaturated aldehydes has been developed. The organic co‐catalytic system of proline and 1,4‐diazabicyclo[2.2.2]octane (DABCO) enables the asymmetric synthesis of the corresponding N‐Boc‐ and N‐Cbz‐protected β‐amino‐α‐alkylidene‐aldehydes in good to high yields and up to 99% ee. In the case of aza‐MBH‐type addition of enals to phenylprop‐2‐ene‐1‐imines, the co‐catalytic reaction exhibits excellent 1,2‐selectivity. The organo‐co‐catalytic aza‐MBH‐type reaction can also be performed by the direct highly enantioselective addition of α,β‐unsaturated aldehydes to bench‐stable N‐carbamate‐protected α‐amidosulfones to give the corresponding β‐amino‐α‐alkylidene‐aldehydes with up to 99% ee. The organo‐co‐catalytic aza‐MBH‐type reaction is also an expeditious entry to nearly enantiomerically pure β‐amino‐α‐alkylidene‐amino acids and β‐amino‐α‐alkylidene‐lactams (99% ee). The mechanism and stereochemistry of the chiral amine and DABCO co‐catalyzed aza‐MBH‐type reaction are also discussed.     

Organocatalytic Asymmetric Mannich Reactions of 5H‐Oxazol‐4‐ones: Highly Enantio‐ and Diastereoselective Synthesis of Chiral α‐Alkylisoserine Derivatives

The first organocatalytic Mannich reaction of 5H‐oxazol‐4‐ones with various readily prepared aryl‐ and alkylsulfonimides has been developed. Two commercially available pseudoenantiomeric Cinchona alkaloids‐derived tertiary amine/ureas have been demonstrated as the most efficient catalysts to access the opposite enantiomers of the Mannich products with equally excellent enantio‐ and diastereoselectivities. From the Mannich adducts, important α‐methyl‐α‐hydroxy‐β‐amino acid derivatives, such as the α‐methylated C‐13 side chain of taxol and taxotere, can be conveniently prepared.     

Infrared study on in situ polymerization of zinc dimethacrylate in poly(α‐octylene‐co‐ethylene) elastomer

An infrared spectroscopic method was used to follow the course of in situ polymerization of zinc dimethacrylate (ZDMA) in poly(α‐octylene‐co‐ethylene) elastomer (POE). The integral intensity of the 831 cm^?1 band, ie the out‐of‐plane deformation mode of ?CH, was used to determine the residual amount of ZDMA in composites cured at 165°C for different times, through which the course of in situ polymerization of ZDMA in POE was traced and the dynamic curve determined. The curing course of the ZDMA/POE/peroxide system at 165°C was examined with a rheometer and compared with the course of in situ polymerization. The results surprisingly show that the in situ polymerization of ZDMA is almost complete at the beginning stage of curing, and that substantial crosslinking starts subsequently. Scanning electron microscopy and transmission electron microscopy observations on morphologies of ZDMA/POE composites cured at 165°C for different times were carried out and confirmed the results of infrared experiments. Combining all the investigations, it was deduced that a competition exists between in situ polymerization and crosslinking in the composites. Covalent crosslinking rather than ionic bond crosslinks are the major types of crosslinks structures in ZDMA/POE composites, and its total density is lower than that of carbon‐ black‐reinforced POE. Copyright © 2004 Society of Chemical Industry     

Ionic Liquid, 1‐n‐Butyl‐3‐methylimidazolium Bis(trifluoromethanesulfonyl)imide,Resulted in the First Catalyst‐Free Aminohalogenation of Electron‐Deficient Alkenes

The 2‐Ns‐based aminohalogenation of α,β‐unsaturated ketones has been achieved in an ionic liquid, 1‐n‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide {[bmim][N(SO₂CF₃)₂]}. [Bmim][N(SO₂CF₃)₂] was found to be superior not only to classical organic solvents but also to its counterpart, [bmim][BF₄], which was proven to be successful in the TsNCl₂‐based aminohalogenation but failed to give any product for this reaction. The present process takes the advantage of 2‐NsNCl₂ as the stable nitrogen/halogen source in a one‐pot operation without the use of any metal catalysts, it is convenient to perform without special protection of inert gases. Eight examples were examined with good to excellent stereoselectivity (1:5 to one isomer) and modest to good chemical yields (53–72 %).     

Bis(3,5‐dimethylphenyl)‐(S)‐pyrrolidin‐2‐ylmethanol: an Improved Organocatalyst for the Asymmetric Epoxidation of α,β‐Enones

The asymmetric epoxidation of α,β‐enones by the readily available bis(3,5‐dimethylphenyl)‐(S)‐pyrrolidin‐2‐ylmethanol and tert‐butyl hydroperoxide (TBHP) is described. Stereoelectronic substitution on the aryl moiety of diaryl‐2‐pyrrolidinemethanols was found to significantly affect the efficiency with respect to the previously reported (S)‐diphenyl‐2‐pyrrolidinemethanol. Improved reactivity and enantioselectivity were achieved with bis(3,5‐dimethylphenyl)‐(S)‐pyrrolidin‐2‐ylmethanol at reduced catalyst loading (20 mol %) with ees up to 94% for chalcone epoxides under mild reaction conditions, whereas (S)‐diphenyl‐2‐pyrrolidinemethanol afforded a maximum ee of 80%. Interestingly, the methodology is applicable to the epoxidation of more challenging aliphatic or enolizable enones with good control of the asymmetric induction (up to 87% ee).