On the Gevrey regularity for Sums of Squares of vector fields, study of some models

The micro-local Gevrey regularity of a class of "sums of squares" with real analytic coefficients is studied in detail. Some partial regularity result is also given

(SEMI-)GLOBAL ANALYTIC HYPOELLIPTICITY FOR A CLASS OF "SUMS OF SQUARES" WHICH FAIL TO BE LOCALLY ANALYTIC HYPOELLIPTIC

The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced by P. Albano, A. Bove, and M. Mughetti, satisfying the Ho spacing diaeresis rmander condition and which fail to be either locally or microlocally analytic hypoelliptic

Sulla regolarità delle soluzioni e dei vettori analitici per “somme di quadrati”

We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type. Moreover we also illustrate a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type, thus providing a microlocal version, in the analytic category, of a result due to M. Derridj.Presentiamo una breve rassegna di alcuni recenti risultati riguardanti la regolarità locale e globale delle soluzioni per alcune classi/modelli di somme di quadrati di campi vettoriali con coefficienti reali analitici a valori reali di tipo H"ormander. Illustriamo anche un risultato riguardante la regolarità microlocale dei vettori analitici per operatori somme di quadrati di campi vettoriali con coefficienti reali analitici a valori reali di tipo H"ormander, fornendo così una versione microlocale, nel caso analitico, di un risultato dovuto a M. Derridj

Error Classification and Reduction in Solid State Qubits

Quantum computers have enormous advantages over classical computers. A quantum computer can be used to calculate the factors of a number, which is sometimes impossible during one\u27s lifetime with a classical computer. Quantum information processing techniques can also be used for encryption, which makes eavesdropping impossible. Noise from the environment is a great challenge in building a reliable quantum computer. To build a reliable quantum computer, one has to protect the information content of the system from the environment. Otherwise, the information associated with the system will decay as the system interacts with the environment. The noise resulting from the system-bath interaction can be removed by using quantum error correcting codes or decoupling pulses. In addition, one could also use DFS encoding to make the information content of the system immune to the noise. In this paper, the various types of errors that could arise in a specific DFS encoding of a 3 spin qubit have been classified according to their effect on the state of the qubit. Also, the application of a specific decoupling pulse on the system, which is coupled to the environment through hyperfine Hamiltonian, has been analyzed

Exploring new chemical entities from traditional medicine: Docking, synthesis and specific bioactivities

Traditional medical systems contributed significantly to medicine with a number of their phytochemicals found to possess good biological properties. Recently, Dr. Youyou Tu was awarded the Nobel Prize (2015) for her discovery/isolation of Artemisinin from the TCM plant Artemisia annua. Our first aim is to identify active phytochemicals against botulinum neurotoxin A (BoNT/A), and diabetes from Ayurveda and TCM, respectively, by using in silico, in vitro and in vivo approaches. In our second aim, we wanted to enantioselectively synthesize scalable quantities of phytoestrogenic isoflavans such as equol and sativan. The following three chapters summarize results of the three research goals. Chapter II describes our approach to identify the small molecules effective against BoNT/A, one of the most lethal toxins known to humans, with none of the current known its inhibitors reaching even the clinical trial stages. Ayurvedic literature was analyzed and a number of plants were identified based on their usage, frequency and utility in various formulations, for treating diseases with symptoms similar to botulism. The phytochemicals of these plants were studied by docking into the catalytic domain of BoNT/A. From the docking results, thirty-one compounds and their analogues were identified and tested in vitro using liquid chromatography-based protease assay. From these results, seven compounds were further tested using ex vivo mouse phrenic nerve hemidiaphragm assay (MPNHDA). Results shoa number of compounds including acoric acid 1, and galangin 3 possessed inhibitory activities of around 40-50% against BoNT/A in the in vitro assay, and in the MPNHDA, initial studies shothat at 20 μM, acoric acid 1 possessed marginal protection. Further testing of the active compounds like acoric acid 1 and their analogues and using more sensitive, reproducible bioassays could yield more active compounds. Chapter III deals with the identification of small-molecule antidiabetic compounds from the TCM plant, Goji (Lycium barbarum and Lycium chinense), widely used for treating various diseases including diabetes and hypertension Current clinical antidiabetic drugs, like rosiglitazone display severe side effects like edema, weight gain and heart failure. By docking the twenty-seven selected reported compounds of Goji into the partial and full agonist binding sites of PPARγ (target of rosiglitazone), tyramine derivatives were found to possess good docking scores and binding poses. Henceforth, twenty-four cinnamomyl phenylethyl amide derivatives (termed as tyramine-derivatives) were synthesized and were tested in vitro using PPARγ-PPARα luciferase assay. Three compounds shosimilar or higher fold induction than the positive control, rosiglitazone. One tyramine-derivative 08, and tyramine derivatives-enriched fraction (21%) of the root bark of L. chinense were further studied in vivo using diabetic db/db mice. However, both of them did not possess antidiabetic properties in the tested mice model. In vivo results indicate that the antidiabetic property of Lycium species is not due to tyramine derivatives. Chapter IV describes the first large-scale, enantioselective synthesis of both antipodes of phytoestrogenic isoflavans, equol and sativan, synthesized in \u3e98% ee, with good overall yields starting from the commercially available starting material. Syntheses of these isoflavans were performed using Evans’ aldol condensation as a chiral inducing step at C-3 position of isoflavan scaffold. The same flexible methodology can be applied for syntheses of other C-3 chiral isoflavans

On the microlocal regularity of the analytic vectors for "sums of squares" of vector fields

We prove via FBI-transform a result concerning the microlocal Gevrey regularity of analytic vectors for operators sums of squares of vector fields with real-valued real analytic coefficients of Hormander type, thus providing a microlocal version, in the analytic category, of a result due to Derridj (Pac J Math 302(2):511-543, 2019) concerning the problem of the local regularity for the Gevrey vectors for sums of squares of vector fields with real-valued real analytic/Gevrey coefficients