Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Unconditional convergence and invertibility of multipliers

In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or necessary conditions for unconditional convergence and invertibility are determined depending on the properties of the analysis and synthesis sequences, as well as the symbol. Examples which show that the given assertions cover different classes of multipliers are given. If a multiplier is invertible, a formula for the inverse operator is determined. The case when one of the sequences is a Riesz basis is completely characterized.Comment: 31 pages; changes to previous version: 1.) the results from the previous version are extended to the case of complex symbols m. 2.) new statements about the unconditional convergence and boundedness are added (3.1,3.2 and 3.3). 3.) the proof of a preliminary result (Prop. 2.2) was moved to a conference proceedings [29]. 4.) Theorem 4.10. became more detaile

Brief for Plaintiff-Appellee, Carroll v. Trump, No. 20-3977 (2nd Cir. Apr. 16, 2021)

Introduction In June 2019, E. Jean Carroll revealed that former President Donald J. Trump had sexually assaulted her decades earlier. Trump denied it, saying he did not know who Carroll was and had never met her. But he did not stop there. He launched a series of vicious, personal attacks. He implied that she was too ugly to rape; that she had falsely accused other men of sexual assault; and that she had invented her story for money, or to sell books, or to advance a political plot. None of this was true. Trump knew that he had assaulted Carroll. He knew who she was. And he knew what he was doing when he went on a defamation rampage designed to crush her— to punish and retaliate against her—for daring to reveal his decades-old crime. Faced with this staggering onslaught, Carroll sought relief in court and sued Trump for defamation. Her case proceeded in New York state court for ten months. Trump did everything he could to stall, but his efforts ultimately failed. Just as the parties were about to engage in merits discovery, the White House prevailed upon the Department of Justice (DOJ) to intercede. Following a certification under the Westfall Act, 28 U.S.C. § 2679(d), DOJ lawyers removed the case to federal court and sought to substitute the United States as the defendant. They took the position that Trump was just doing his job—i.e., that he was acting within the scope of his employment—when he repeatedly slandered a private citizen who was no longer willing to hide the fact that he had raped her long before taking office. On two separate grounds, Judge Kaplan denied DOJ’s motion to substitute. He first held that the statute invoked by DOJ in support of substitution—the Federal Tort Claims Act (FTCA), 28 U.S.C. §§ 1346, 2671, as amended by the Westfall Act—does not apply to the President. That conclusion is compelled by the FTCA’s text and structure, as well as a host of constitutional, legislative, and judicial authorities, all of which confirm that the FTCA does not apply to the President. On appeal, DOJ (joined by Trump) seeks to show otherwise, but their arguments make a mess of the statute and offend settled separation-of-powers principles. In the alternative, Judge Kaplan concluded Trump was not acting within the scope of his employment when he defamed Carroll. This commonsense conclusion follows directly from the evidence before the Court and from longstanding principles of respondeat superior liability. On appeal, DOJ and Trump offer no basis to disturb that finding. Indeed, there is almost nothing in their briefs that discusses the facts at all. Instead, they urge the Court to adopt a new rule that would create categorical immunity for any federal official who defames anyone while speaking to the press or responding to perceived critics. That rule is both wrong and dangerous, and this Court should reject Appellants’ effort to avoid answering for Trump’s conduct. “Public office does not carry with it a license to defame at will, for even the highest officers exist to serve the public, not to denigrate its members.” Clark v. McGee, 49 N.Y.2d 613, 618-19 (1980). If accepted, Appellants’ extreme position would distort precedent, dishonor the Office of the Presidency, and give succor to the view that our most powerful political leaders stand entirely above the law. This Court should therefore affirm the denial of DOJ’s motion to substitute. Statement of the issues: 1. Is the President an “employee of the government” as that term is defined in the Federal Tort Claims Act (FTCA), 28 U.S.C. § 2671? 2. Assuming the President is an “employee of the government” under the FTCA, did Donald J. Trump act within the scope of his employment when he subjected E. Jean Carroll to willful, outrageous defamatory attacks in retaliation for revealing that he had sexually assaulted her decades before he was elected President

A One-sided, Highly Relativistic Jet from Cygnus X-3

Very Long Baseline Array images of the X-ray binary, Cygnus X-3, were obtained 2, 4 and 7 days after the peak of a 10 Jy flare on 4 February 1997. The first two images show a curved one-sided jet, the third a scatter-broadened disc, presumably at the position of the core. The jet curvature changes from the first to the second epoch, which strongly suggests a precessing jet. The ratio of the flux density in the approaching to that in the (undetected) receding jet is > 330; if this asymmetry is due to Doppler boosting, the implied jet speed is > 0.81c. Precessing jet model fits, together with the assumptions that the jet is intrinsically symmetric and was ejected during or after the major flare, yield the following constraints: the jet inclination to the line of sight must be < 14 degrees; the cone opening angle must be < 12 degrees; and the precession period must be > 60 days.Comment: 12 pages 7 figures, accepted by Ap

Noninnocent Dithiolene Ligands: A New Oxomolybdenum Complex Possessing a Donor-Acceptor Dithiolene Ligand

A new monoanionic dithiolene ligand is found in Tp*MoO(S(2)BMOQO). A combination of x-ray crystallography, electronic absorption and resonance Raman spectroscopies, and bonding calculations reveal that the monoanionic dithiolene ligand possesses considerable thiolate-thione character resulting from admixture of an intraligand charge transfer excited state into the ground state wavefunction. The unusual dithiolene exhibits a highly versatile donor-acceptor character that dramatically lowers the Mo(IV/V) redox couple and points to a potentially non-innocent role of the pterin fragment in pyranopterin Mo enzymes. [Image: see text

A Study of Mo(4+)Quinoxalyl-Dithiolenes as Models for the Non-Innocent Pyranopterin in the Molybdenum Cofactor

A model system for the molybdenum cofactor has been developed that illustrates the noninnocent behavior of an N-heterocycle appended to a dithiolene chelate on molybdenum. The pyranopterin of the molybdenum cofactor is modeled by a quinoxalyldithiolene ligand (S(2)BMOQO) formed from the reaction of molybdenum tetrasulfide and quinoxalylalkyne. The resulting complexes TEA[Tp*MoX(S(2)BMOQO)] [1, X = S; 3, X = O; TEA = tetraethylammonium; Tp* = hydrotris(3,5-dimethylpyrazolyl)borate] undergo a dehydration-driven intramolecular cyclization within quinoxalyldithiolene, forming Tp*MoX(pyrrolo-S(2)BMOQO) (2, X = S; 4, X = O). 4 can be oxidized by one electron to produce the molybdenum(5+) complex 5. In a preliminary report of this work, evidence from X-ray crystallography, electronic absorption and resonance Raman spectroscopies, and density functional theory (DFT) bonding calculations revealed that 4 possesses an unusual asymmetric dithiolene chelate with significant thione-thiolate character. The results described here provide a detailed description of the reaction conditions that lead to the formation of 4. Data from cyclic voltammetry, additional DFT calculations, and several spectroscopic methods (IR, electronic absorption, resonance Raman, and electron paramagnetic resonance) have been used to characterize the properties of members in this suite of five Mo(S(2)BMOQO) complexes and further substantiate the highly electron-withdrawing character of the pyrrolo-S(2)BMOQO ligand in 2, 4, and 5. This study of the unique noninnocent ligand S(2)BMOQO provides examples of the roles that the N-heterocycle pterin can play as an essential part of the molybdenum cofactor. The versatile nature of a dithiolene appended by heterocycles may aid in modulating the redox processes of the molybdenum center during the course of enzyme catalysis

A Study of Mo(4+)Quinoxalyl-Dithiolenes as Models for the Non-Innocent Pyranopterin in the Molybdenum Cofactor

A model system for the molybdenum cofactor has been developed that illustrates the noninnocent behavior of an N-heterocycle appended to a dithiolene chelate on molybdenum. The pyranopterin of the molybdenum cofactor is modeled by a quinoxalyldithiolene ligand (S(2)BMOQO) formed from the reaction of molybdenum tetrasulfide and quinoxalylalkyne. The resulting complexes TEA[Tp*MoX(S(2)BMOQO)] [1, X = S; 3, X = O; TEA = tetraethylammonium; Tp* = hydrotris(3,5-dimethylpyrazolyl)borate] undergo a dehydration-driven intramolecular cyclization within quinoxalyldithiolene, forming Tp*MoX(pyrrolo-S(2)BMOQO) (2, X = S; 4, X = O). 4 can be oxidized by one electron to produce the molybdenum(5+) complex 5. In a preliminary report of this work, evidence from X-ray crystallography, electronic absorption and resonance Raman spectroscopies, and density functional theory (DFT) bonding calculations revealed that 4 possesses an unusual asymmetric dithiolene chelate with significant thione-thiolate character. The results described here provide a detailed description of the reaction conditions that lead to the formation of 4. Data from cyclic voltammetry, additional DFT calculations, and several spectroscopic methods (IR, electronic absorption, resonance Raman, and electron paramagnetic resonance) have been used to characterize the properties of members in this suite of five Mo(S(2)BMOQO) complexes and further substantiate the highly electron-withdrawing character of the pyrrolo-S(2)BMOQO ligand in 2, 4, and 5. This study of the unique noninnocent ligand S(2)BMOQO provides examples of the roles that the N-heterocycle pterin can play as an essential part of the molybdenum cofactor. The versatile nature of a dithiolene appended by heterocycles may aid in modulating the redox processes of the molybdenum center during the course of enzyme catalysis

Parameters for Successful Parental RNAi as An Insect Pest Management Tool in Western Corn Rootworm, \u3ci\u3eDiabrotica virgifera virgifera\u3c/i\u3e

Parental RNAi (pRNAi) is an RNA interference response where the gene knockdown phenotype is observed in the progeny of the treated organism. pRNAi has been demonstrated in female western corn rootworms (WCR) via diet applications and has been described as a potential approach for rootworm pest management. However, it is not clear if plant-expressed pRNAi can provide effective control of next generation WCR larvae in the field. In this study, we evaluated parameters required to generate a successful pRNAi response in WCR for the genes brahma and hunchback. The parameters tested included a concentration response, duration of the dsRNA exposure, timing of the dsRNA exposure with respect to the mating status in WCR females, and the effects of pRNAi on males. Results indicate that all of the above parameters affect the strength of pRNAi phenotype in females. Results are interpreted in terms of how this technology will perform in the field and the potential role for pRNAi in pest and resistance management strategies. More broadly, the described approaches enable examination of the dynamics of RNAi response in insects beyond pRNAi and crop pests

Parameters for Successful Parental RNAi as An Insect Pest Management Tool in Western Corn Rootworm, \u3ci\u3eDiabrotica virgifera virgifera\u3c/i\u3e

Parental RNAi (pRNAi) is an RNA interference response where the gene knockdown phenotype is observed in the progeny of the treated organism. pRNAi has been demonstrated in female western corn rootworms (WCR) via diet applications and has been described as a potential approach for rootworm pest management. However, it is not clear if plant-expressed pRNAi can provide effective control of next generation WCR larvae in the field. In this study, we evaluated parameters required to generate a successful pRNAi response in WCR for the genes brahma and hunchback. The parameters tested included a concentration response, duration of the dsRNA exposure, timing of the dsRNA exposure with respect to the mating status in WCR females, and the effects of pRNAi on males. Results indicate that all of the above parameters affect the strength of pRNAi phenotype in females. Results are interpreted in terms of how this technology will perform in the field and the potential role for pRNAi in pest and resistance management strategies. More broadly, the described approaches enable examination of the dynamics of RNAi response in insects beyond pRNAi and crop pests

Netrin-3: Tracking the Elusive Antimitotic Signal on the Western Frontier

Netrin-3 is a guidance protein expressed throughout the animal kingdom, and involved in the development of branched structures such as the nervous system, lung, and mammary gland. We have previously shown that peptides derived from this protein serve as chemorepellents and mitotic inhibitors in Tetrahymena thermophila. Our previous work shows that Tetrahymena synthesize and secrete a netrin-3-like protein, as detected by ELISA. In this study, we find that a netrin-3-like protein is present in whole cell extract and secreted protein, as detected by Western blotting. A protein of approximately 48 kD is consistently detected in our Western blots. In addition, we often detect a protein of 52 kD, which may be the netrin-1-like protein of Tetrahymena that we have previously described. Further studies will enable us to determine whether the 52-kD protein is indeed the netrin-1 like protein of Tetrahymena