Asymptotic properties of the maximum likelihood estimate in the first order autoregressive process

Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE) based onT observations from the first order Gaussian process up to the term of orderT ⁻¹. The expansion is used to compare with a generalized estimate including the least square estimate (LSE) , based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT ⁻¹. It is shown that (or the modified MLE ) is better than (or the modified estimate ). Further, we note that does not attain the bound for third order asymptotic median unbiased estimates.     

Stereocontrolled synthesis of steroid side chain; stereoselective syntheses of cholesterol and 25-hydroxycholesterol

Novel stereoselective method to introduce side chain onto 17-oxosteroids has been deviced, and using the method cholesterol and 25-hydroxycholesterol are synthesized.     

Phosphazene Base tBu-P4 Catalyzed Methoxy–Alkoxy Exchange Reaction on (Hetero)Arenes

The organic superbase tBu-P4 catalyzes methoxy-alkoxy exchange reactions on (hetero)arenes with alcohols. The catalytic reaction proceeded efficiently with electron-deficient methoxy(hetero)arenes as well as with a variety of alcohols, including 3-amino-1-propanol, β-citronellol, menthol, and cholesterol. An intramolecular version of this reaction furnished six- and seven-membered ring compounds.     

Synthesis and Spectroscopic Studies of Arylethynylsilanes

A variety of arylethynylsilanes (Ar‐C?C? C₆H₄? C?C)_nSiMe_4?n were prepared successfully by reaction of the corresponding chlorosilanes Me_4?nSiCl_n with Ar? C?C? C₆H₄? C?CM (M=Li, MgBr), which was prepared by treatment of ethynyl(diarylethyne)s Ar? C?C? C₆H₄? C?CH with BuLi or MeMgBr. The ethynyl(diarylethyne)s were readily prepared in good yields by the double‐elimination method: addition of lithium hexamethyldisilazide to a mixture of ArCH₂SO₂Ph, TMS? C?C? C₆H₄? CHO, and ClP(O)(OEt)₂, followed by desilylation. In the tetrakis(arylethynyl)silanes (Ar? C?C? C₆H₄? C?C)₄Si thus prepared, through‐space conjugation of four triple bonds on the silicon atom emerges as a result of participation of the silicon orbitals in the acetylenic π orbitals. This participation enhances the emissive quantum yields of arylethynylsilanes with an increase in the number of arylethynyl moieties on silicon: quantum yields of emission (Φ_F) of 0.72 for (MeOC₆H₄? C?C? C₆H₄? C?C)₄Si, 0.53 for (MeOC₆H₄? C?C? C₆H₄? C?C)₂SiMe₂, and 0.47 for MeO‐C₆H₄? C?C? C₆H₄? C?CSiMe₃ were obtained. Although this enhancement effect was also observed in the phenylethynylarylsilane (MeOC₆H₄? C?C? C₆H₄)₂SiMe₂, the bis(arylethynyl)disilane (MeOC₆H₄? C?C? C₆H₄? C?C‐SiMe₂)₂ exhibited non‐enhanced emission.     

Direct Carboxylation of Electron-Rich Heteroarenes Promoted by LiO-tBu with CsF and [18]Crown-6

We herein demonstrate that the combination of LiO-tBu, CsF, and [18]crown-6 efficiently promotes the direct C−H carboxylation of electron-rich heteroarenes (benzothiophene, thiophene, benzofuran, and furan derivatives). A variety of functional groups, including methyl, methoxy, halo, cyano, amide, and keto moieties, are compatible with this system. The reaction proceeds via the formation of a tert-butyl carbonate species.     

Octapalladium Strings Trap C60 and C70 Fullerenes Affording Metal-Chain-Wired Bucky Balls

Reactions of Pd₈ strings supported by meso-Ph₂PCH₂P(Ph)CH₂P(Ph)CH₂PPh₂ (meso-dpmppm) ligands, [Pd₈(meso-dpmppm)₄(L)₂]⁴⁺ (L=CH₃CN ( 1 ), XylNC ( 2 )) with C₆₀ resulted in the exclusive formation of unprecedented metal-chain-wired C₆₀ bucky balls, [{Pd₄(meso-dpmppm)₂(L)}₂(C₆₀)]⁴⁺ (L=CH₃CN ( 11 ), XylNC ( 12 )), in which a C₆₀ fullerene is trapped in the central Pd–Pd junction, as unambiguously established by spectroscopic, X-ray crystallographic, and theoretical techniques. The similar reaction of Pd₈ strings supported by rac-dpmppm, [Pd₈(rac-dpmppm)₄(CH₃CN)₂]⁴⁺ ( 3 ) also afforded a racemic mixture of [{Pd₄((R*,R*)-dpmppm)₂(CH₃CN)}₂(C₆₀)]⁴⁺ ( 13 ) without scrambling the Pd₄ fragments with (R,R)- and (S,S)-dpmppm ligands. Consequently, those of enantiopure chiral Pd₈ strings, [Pd₈((R*,R*)-dpmppm)₄(CH₃CN)₂]⁴⁺, certainly afforded chiral bucky balls of [{Pd₄((R*,R*)-dpmppm)₂(CH₃CN)}₂(C₆₀)]⁴⁺ ( 13 _RR and 13 _SS ), that exhibit mirror-image circular dichroism spectra. The reactions of 1 and 2 were also applied for trapping a C₇₀ fullerene to give 2 : 1 adducts of [{Pd₄(meso-dpmppm)₂(L)}₂(C₇₀)]⁴⁺ (L=CH₃CN ( 21 ), XylNC ( 22 )). These results provide useful information for creating a platform to develop dimensionally and chirality controlled metal–carbon nanocomposite materials.     

Glycosylated tris-bipyridine ferrous complexes as molecular mimics of densely packed glycoclusters on cell surfaces: spatial carbohydrate packing of glycoclusters changes on additions of salts

Tris-bipyridine ferrous complexes having β-lactosides, β-maltosides or α-mannosides with serinol spacers were prepared as molecular mimics of densely packed carbohydrate clusters on cell surfaces. Conformational analysis on these glycosylated complexes were conducted by UV–vis and circular dichroism spectroscopy measurements, which disclosed that the chloride, nitrate and sulfate salts induced the conformational changes of the glycosylated complexes in the anion- and carbohydrate-dependent manners.     

Photoinduced addition and addition–elimination reactions of perfluoroalkyl iodides to electron-deficient olefins

Photoinduced radical perfluoroalkylation of various simple electron-deficient olefins was achieved in the presence of an aqueous Na₂S₂O₃ solution. The reactions proceeded smoothly to give addition or addition–elimination products. The ability of the products to be used as radical precursors or Michael acceptors was also demonstrated.     

Combined two-dimensional velocity and temperature measurements using a high-speed camera and luminescent particles

This paper proposes a combined method for two-dimensional temperature and velocity measurements using temperature sensitive particles (TSParticles), a pulsed ultraviolet (UV) laser and a single high-speed camera. TSParticles were synthesized using ion-exchange particles and Eu(TTA) luminescent dye. The size and material of the particles for synthesizing TSParticles are selectable. TSParticles respond to temperature changes in a flow and can also serve as tracers for the velocity field. TSParticles were seeded into a heated water flow in a complex-shaped channel constructed of MEXFLON resin, which has a refractive index exactly equal to that of water. Particle images of flow beyond the structure can be recorded without any distortion. The TSParticles were excited by the UV pulsed laser and the luminescence from the TSParticles were recorded at 40,000 frames per second as sequential images for a lifetime-based temperature analysis. Another advantage of our approach is that high time-resolved PIV can be carried out without a high-frequency laser. The recorded images were also used for the particle image velocimetry (PIV) calculation.