Arithmetic degree and associated graded modules

We prove that the arithmetic degree of a graded or local ring A is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideal I in A. In particular, if Spec(A) is equidimensional and has an embedded component (i.e., A has an embedded associated prime ideal), then the normal cone of Spec(A) along V(I) has an embedded component too. This extends a result of W. M. Ruppert about embedded components of the tangent cone.Mathematics Subject Classification (2000): Primary 13H15, 13A30; Secondary 13D45, 14Q99     

Performance evaluation of fiber Bragg grating sensors by digital holographic technique, strain gauge measurement

In view of the growing interest for non-destructive tests of materials, geodynamical monitoring and in general remote sensing, there is a great effort to bring practical optical sensors from research labs to industrial and environmental applications. In this paper, we employ digital holographic technique as an efficient tool for evaluating the strain measurement capability of fiber Bragg gratings (FBG). A cantilever beam has been employed as a test structure under loading test. The strain measurements results obtained by fiber-based sensors have been compared to those obtained by using full-field digital holographic technique and point-wise strain gauge sensors glued on the same cantilever beam. A simple theoretical model is also presented to interpret and compare the experimental results coming from different techniques.     

Strength of the trilinear Higgs boson coupling in technicolor models

We discuss the strength of the trilinear Higgs boson coupling in technicolor (or composite) models in a model independent way. The coupling is determined as a function of a very general ansatz for the technicolor self-energy, and turns out to be equal or smaller than the one of the Standard Model Higgs boson depending on the dynamics of the theory.     

Phase separation of p53 precedes aggregation and is affected by oncogenic mutations and ligands

Mutant p53 tends to form aggregates with amyloid properties, especially amyloid oligomers inside the nucleus, which are believed to cause oncogenic gain-of-function (GoF). The mechanism of the formation of the aggregates in the nucleus remains uncertain. The present study demonstrated that the DNA-binding domain of p53 (p53C) underwent phase separation (PS) on the pathway to aggregation under various conditions. p53C phase separated in the presence of the crowding agent polyethylene glycol (PEG). Similarly, mutant p53C (M237I and R249S) underwent PS; however, the process evolved to a solid-like phase transition faster than that in the case of wild-type p53C. The data obtained by microscopy of live cells indicated that transfection of mutant full-length p53 into the cells tended to result in PS and phase transition (PT) in the nuclear compartments, which are likely the cause of the GoF effects. Fluorescence recovery after photobleaching (FRAP) experiments revealed liquid characteristics of the condensates in the nucleus. Mutant p53 tended to undergo gel- and solid-like phase transitions in the nucleus and in nuclear bodies demonstrated by slow and incomplete recovery of fluorescence after photobleaching. Polyanions, such as heparin and RNA, were able to modulate PS and PT in vitro. Heparin apparently stabilized the condensates in a gel-like state, and RNA apparently induced a solid-like state of the protein even in the absence of PEG. Conditions that destabilize p53C into a molten globule conformation also produced liquid droplets in the absence of crowding. The disordered transactivation domain (TAD) modulated both phase separation and amyloid aggregation. In summary, our data provide mechanistic insight into the formation of p53 condensates and conditions that may result in the formation of aggregated structures, such as mutant amyloid oligomers, in cancer. The pathway of mutant p53 from liquid droplets to gel-like and solid-like (amyloid) species may be a suitable target for anticancer therapy.

Mutant p53 tends to form aggregates with amyloid properties, especially amyloid oligomers inside the nucleus, which are believed to cause oncogenic gain-of-function (GoF).     

Optically activated functionalization reactions in Si quantum dots

Using ab initio calculations, we have studied the influence of optical activation on functionalization reactions of silicon quantum dots with unsaturated hydrocarbons. We find that the energy barrier for the replacement of silicon-hydrogen with silicon-carbon bonds is dramatically reduced if the silicon dot is optically excited. These results provide an explanation for recent experiments on optically excited porous silicon. In addition, our calculations point at the existence of an intermediate spin-polarized state formed by the dot and an alkene or alkyne, upon relaxation after absorbing a photon. This state could be detected experimentally, by, for example, electron spin resonance measurements. Based on the results of our calculations as a function of the dot size, varied from 0.8 to 1.5 nm, we propose that light activated reactions could be used to functionalize and size select silicon quantum dots at the same time.     

Preparation and self-assembly of chiral porphyrin diads on the gold electrodes of quartz crystal microbalances: a novel potential approach to the development of enantioselective chemical sensors

Porphyrin diad 1 was synthesized by reaction of the acyl chloride of porphyrin 2 and trans-1,2-dithiane-4,5-diol. The Co complex of this diad was studied as a potential enantioselective receptor for chiral recognition in solution and in the solid state. In solution both enantiomers of limonene induce significant changes in the visible and circular dichroism (CD) spectra of [Co2(1)], while a different behavior is observed in the case of the enantiomeric pair of trans-1,2-diaminocyclohexane. A different efficiency of [Co2(1)] chiral recognition is obtained for these compounds, with a remarkable degree of enantiodiscrimination observed in the case of limonene. Self-assembled monolayers of [Co2(1)] were deposited onto the gold electrodes of quartz crystal microbalances to be used as sensing materials of nanogravimetric sensors operating in the gas phase. The enantiodiscrimination properties of these sensors towards the enantiomeric pairs of chiral analytes have been studied. While in the case of analytes bearing donor ligand atoms we did not observe a remarkable enantioselectivity, a significant degree of chiral discrimination was observed in the case of limonene; this result is particularly encouraging for the potential development of enantioselective chemical sensors for use in an array configuration.     

Reaction of dichloroketene and sulfene with N,N-disubstituted α-aminomethyleneketones. Synthesis of pyrano[2,3-e]indazole and 1,2-oxathiino[6,5-e]indazole derivatives

The polar 1,4-cycloaddition of dichloroketene to N,N-disubstituted (E)-5-aminomethylene-1,5,6,7-tetrahydro-(1-methyl)(1-phenyl)-4H-indazol-4-ones V, prepared from 1,5,6,7-tetrahydro-(1-methyl)(1-phenyl)-4H-indazol-4-ones via the 5-hydroxymethylene derivatives, gave in good yield N,N-disubstituted 4-amino-3,3-dichloro-4,5,6,7-tetrahydro-(7-methyl)(7-phenyl)pyrano[2,3-e]indazol-(3H)ones VI, which are derivatives of the new heterocyclic system pyrano[2,3-e]indazole. Dehydrochlorination of VI with DBN afforded N,N-disubstituted 4-amino-3-chloro-6,7-dihydro(7-methyl)(7-phenyl)pyrano[2,3-e]indazol-2(5H]-ones VII generally in satisfactory yield. Full aromatization with DDQ of VII was tried only in the case of dimethylamino derivatives, giving a moderate yield of 3-chloro-4-dimethylamino(7-methyl)(7-phenyl)pyrano[2,3-e]indazol-2(7H)-ones. Cycloaddition of sulfene to V occurred only in the case of aliphatic N-substitution to give in moderate yield 4-dialkylamino-4,5,6,7-tetrahydro-(7-methyl)(7-phenyl)-3H-1,2-oxathiino[6,5-e]indazole 2,2-dioxides, which are derivatives of the new heterocyclic system 1,2-oxathiino[6,5-e]indazole.     

Diheteroarylmethanes. 6.(1) Probing the Electron-Withdrawing Rank of Heteroaryl Groups by Conformational Studies of Push-Pull Ethylenes. Isolation of NH-Enamine Tautomers of alpha,alpha-Diheteroarylacetaldehydes (Heteroaryl = 2-Benzoxazolyl, 2-Benzothiazolyl)

Enamines and enol ethers substituted in the beta position by the 2-benzoxazolyl and 2-benzothiazolyl group have been obtained by condensing dimethylformamide dimethyl acetal and ethyl orthoformate, respectively, with bis(2-benzoxazolyl)methane and bis(2-benzothiazolyl)methane. A dynamic NMR and semiempirical (PM3) investigation on rotational energy barriers has been carried out in order to rank the electron-withdrawing capacity of the heterocyclic rings. The NMR-based evaluation of the energy barriers corresponding to the rotation along the enaminic double bond has shown that the pi-electron-withdrawing power of benzothiazole is larger than that of benzoxazole, in full accord with previously obtained charge demand values based on (13)C and (15)N pi-charge/shift relationships. The NMR and the computational approaches have led to consistent results. The X-ray crystal structure of alpha,alpha-bis(2-benzothiazolyl)-beta-(dimethylamino)ethene shows that only one heteroaryl ring is coplanar with the enaminic double bond, while the second one is twisted by 73 degrees relative to such a plane. Moreover, in this case calculations closely reproduce the experimental results. In the calculated transition states corresponding to the rotational process along the enamine double bond, the two heteroaryl groups become coplanar and conjugation develops between the enaminic nitrogen electron pool and both heterocycles. The lower rotational barrier observed in the case of the 2-benzothiazolyl derivatives, with respect to the 2-benzoxazolyl derivatives, is therefore a direct consequence of the higher electron-withdrawing power of the former group. Furthermore, a stabilizing intramolecular nonbonded S.S interaction in the rotational transition state of the benzothiazolyl derivatives is evidenced by the calculations. An unprecedented isolation of the NH-enamine tautomer involving the benzoxazolyl and benzothiazolyl ring in alpha,alpha-diheteroacetaldehydes has been performed, confirming these heterocycles as strong electron-withdrawing substituents.