Families of spectral sets for Bernoulli convolutions

In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For other cases, we exhibit maximal Fourier families that are not orthonormal bases.Comment: 25 pages, same result

Additive spectra of the 1/4 Cantor measure

In this paper, we add to the characterization of the Fourier spectra for Bernoulli convolution measures. These measures are supported on Cantor subsets of the line. We prove that performing an odd additive translation to half the canonical spectrum for the 1/4 Cantor measure always yields an alternate spectrum. We call this set an additive spectrum. The proof works by connecting the additive set to a spectrum formed by odd multiplicative scaling.Comment: 9 pages, 1 figur

Optimization of diarylazines as anti-HIV agents with dramatically

Non-nucleoside inhibitors of HIV-1 reverse transcriptase are reported that have ca. 100-fold greater solubility than the structurally related drugs etravirine and rilpivirine, while retaining high anti-viral activity. The solubility enhancements come from strategic placement of a morpholinylalkoxy substituent in the entrance channel of the NNRTI binding site. Compound 4d shows low-nanomolar activity similar to etravirine towards wild-type HIV-1 and key viral variants.Fil: Bollini, Mariela. University of Yale; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Cisneros, José A.. University of Yale; Estados UnidosFil: Spasov, Krasimir A.. University of Yale; Estados UnidosFil: Anderson, Karen S.. University of Yale; Estados UnidosFil: Jorgensen, William L.. University of Yale; Estados Unido

Scaling by 5 on a 1/4-Cantor Measure

Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L^2(\mu), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.Comment: 34 page

Effects of carbon incorporation on doping state of YBa2Cu3Oy

Effects of carbon incorporation on the doping state of YBa2Cu3Oy (Y-123) were investigated. Quantitative carbon analysis revealed that carbon could be introduced into Y-123 from both the precursor and the sintering gas. Nearly carbon-free (< 200 ppm) samples were prepared from a vacuum-treated precursor by sintered at 900 &#730;C and cooling with 20 &#730;C /min in flowing oxygen gas. The lower Tc (= 88 K) and higher oxygen content (y = 6.98) strongly suggested the overdoping state, which was supported by the temperature dependence of resisitivity and thermoelectric power. The nuclear quadrapole resonance spectra and the Raman scattering spectra indicated that there was almost no oxygen defect in the Cu-O chain in these samples. On the other hand, in the same cooling condition, the samples sintered in air stayed at optimal doping level with Tc = 93 K, and the intentionally carbon-doped sample was in the underdoping state. It is revealed that about 60% of incorporated carbon was substituted for Cu at the chain site in the form of CO32+, and the rest remains at the grain boundary as carbonate impurities. Such incorporation affected the oxygen absorption process in Y-123. It turned out that the oxygen content in Y-123 cannot be controlled only by the annealing temperature and the oxygen partial pressure but also by the incorporated carbon concentration.Comment: 16pages, 9figure

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Structure-based evaluation of C5 derivatives in the catechol diether series targeting HIV-1 reverse transcriptase

Using a computationally driven approach, a class of inhibitors with picomolar potency known as the catechol diethers were developed targeting the non-nucleoside-binding pocket of HIV-1 reverse transcriptase. Computational studies suggested that halogen-bonding interactions between the C5 substituent of the inhibitor and backbone carbonyl of conserved residue Pro95 might be important. While the recently reported crystal structures of the reverse transcriptase complexes confirmed the interactions with the non-nucleoside-binding pocket, they revealed the lack of a halogen-bonding interaction with Pro95. To understand the effects of substituents at the C5 position, we determined additional crystal structures with 5-Br and 5-H derivatives. Using comparative structural analysis, we identified several conformations of the ethoxy uracil dependent on the strength of a van der Waals interaction with the Cγ of Pro95 and the C5 substitution. The 5-Cl and 5-F derivatives position the ethoxy uracil to make more hydrogen bonds, whereas the larger 5-Br and smaller 5-H position the ethoxy uracil to make fewer hydrogen bonds. EC50 values correlate with the trends observed in the crystal structures. The influence of C5 substitutions on the ethoxy uracil conformation may have strategic value, as future derivatives can possibly be modulated to gain additional hydrogen-bonding interactions with resistant variants of reverse transcriptase.Fil: Frey, Kathleen M.. University of Yale; Estados UnidosFil: Gray, William T.. University of Yale; Estados UnidosFil: Spasov, Krasimir A.. University of Yale; Estados UnidosFil: Bollini, Mariela. University of Yale; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gallardo Macias, Ricardo. University of Yale; Estados UnidosFil: Jorgensen, William L.. University of Yale; Estados UnidosFil: Anderson, Karen S.. University of Yale; Estados Unido

Structural Studies and Structure Activity Relationships for Novel Computationally Designed Non-nucleoside Inhibitors and Their Interactions With HIV-1 Reverse Transcriptase

Reverse transcriptase (RT) from the human immunodeficiency virus continues to be an attractive drug target for antiretroviral therapy. June 2022 will commemorate the 30th anniversary of the first Human Immunodeficiency Virus (HIV) RT crystal structure complex that was solved with non-nucleoside reverse transcriptase inhibitor nevirapine. The release of this structure opened opportunities for designing many families of non-nucleoside reverse transcriptase inhibitors (NNRTIs). In paying tribute to the first RT-nevirapine structure, we have developed several compound classes targeting the non-nucleoside inhibitor binding pocket of HIV RT. Extensive analysis of crystal structures of RT in complex with the compounds informed iterations of structure-based drug design. Structures of seven additional complexes were determined and analyzed to summarize key interactions with residues in the non-nucleoside inhibitor binding pocket (NNIBP) of RT. Additional insights comparing structures with antiviral data and results from molecular dynamics simulations elucidate key interactions and dynamics between the nucleotide and non-nucleoside binding sites.Fil: Frey, Kathleen M.. University of Yale; Estados UnidosFil: Bertoletti, Nicole. University of Yale; Estados UnidosFil: Chan, Albert H.. University of Yale; Estados UnidosFil: Ippolito, Joseph A.. University of Yale; Estados UnidosFil: Bollini, Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias "Elizabeth Jares Erijman"; Argentina. University of Yale; Estados UnidosFil: Spasov, Krasimir A.. University of Yale; Estados UnidosFil: Jorgensen, William L.. University of Yale; Estados UnidosFil: Anderson, Karen S.. University of Yale; Estados Unido

Extension into the entrance channel of HIV-1 reverse transcriptase—Crystallography and enhanced solubility

Non-nucleoside inhibitors of HIV-1 reverse transcriptase (HIV-RT) are reported that feature extension into the entrance channel near Glu138. Complexes of the parent anilinylpyrimidine 1 and the morpholinoethoxy analog 2j with HIV-RT have received crystallographic characterization confirming the designs. Measurement of aqueous solubilities of 2j, 2k, the parent triazene 2a, and other NNRTIs demonstrate profound benefits for addition of the morpholinyl substituent.Fil: Bollini, Mariela. University of Yale; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Frey, Kathleen M.. University of Yale. School of Medicine; Estados UnidosFil: Cisneros, José A.. University of Yale; Estados UnidosFil: Spasov, Krasimir A.. University of Yale. School of Medicine; Estados UnidosFil: Das, Kalyan. Rutgers University; Estados UnidosFil: Bauman, Joseph D.. Rutgers University; Estados UnidosFil: Arnold, Eddy. Rutgers University; Estados UnidosFil: Anderson, Karen S.. University of Yale. School of Medicine; Estados UnidosFil: Jorgensen, William L.. University of Yale; Estados Unido