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Department/Unit poster (BioMolecular Sciences). Corresponding author: Rama S. Gadepalli ([email protected])https://egrove.olemiss.edu/pharm_annual_posters_2022/1008/thumbnail.jp

RIGIDITY RESULTS FOR LICHNEROWICZ BAKRY-EMERY RICCI TENSORS

We investigate rigidity phenomena in the class of Riemannian manifolds with density. By a weighted manifold (or manifold with density) we mean a Riemannian manifold endowed with a weighted measure absolute continuous with respect to the Riemannian one. Associated to a weighted manifold there is also a natural divergence form second order diffusion operator: the f-Laplacian. Good choiches for the concept of curvature in this setting are those that reveal interplays with metric and topological properties of the space. We have focused on Lichnerowicz Bakry-Emery Ricci's tensors. When we impose the constancy of these tensors we are endowing the manifold of an additional structure, namely, a gradient Ricci soliton or a quasi-Einstein structure. The importance of Ricci solitons is due to Perelman's solution of Poincar\ue8 conjecture, while the importance of quasi-Einstein manifolds comes from the relationship they have with Einstein warped products. Actually in this thesis we also introduce an extension of the concept of gradient Ricci soliton, the Ricci almost soliton, allowing the soliton constant to be a generic smooth function on the weighted manifold. In view of the not necessarily constantness, one expects that a certain flexibility on the almost soliton structure is allowed and, consequently, the existence of almost solitons is easier to prove than in the classical situation. This feeling is confirmed by a number of diff erent examples of almost solitons. On the other hand we prove a rigidity result which indicates that almost solitons should reveal a reasonably broad generalization of the fruitful concept of classical soliton. Considering elliptic equations and inequalities (naturally involving the f-Laplacian) for various geometric quantities and making use of analytical techniques coming from stochastic analysis such as stochastic completeness, in the form of the weak Omori-Yau maximum principle, parabolicity and Lp-Liouville type results, we prove rigidity in the form of metric rigidity (scalar curvature estimates, classification results, gap theorems for some geometric quantities) and in the form of triviality of the additional structure. Moreover we obtain also topological rigidity for these tensors (with consequences e.g. on the structure of the fundamental group)

Asymmetric Hydrogenation vs Transfer Hydrogenation in the Reduction of Cyclic Imines

A comparison between the two most common reduction approaches for obtaining chiral amines, asymmetric hydrogenation (AH) versus asymmetric transfer hydrogenation (ATH), was accomplished by using iridium complexes based on atropoisomeric diphosphines and cyclic diamines as ligands respectively. Seven substrates, different in electronic and steric properties, were screened applying both reduction methods. For AH the best results in terms of enantioselectivity (e.e. up to 64%) were obtained by using [Ir(COD)(TetraMe-BITIOP)]Cl in the presence of DCDMH as additive. ATH was carried out with [IrCp*(CAMPY)Cl]Cl as catalyst, allowing the obtainment of the products with appreciable e.e. (up to 76%)

Some triviality results for quasi-Einstein manifolds and Einstein warped products

In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for solutions of weighted Poisson-type equations and adaptations to the weighted setting of some Liouville-type theorems.Comment: 15 pages, fixed minor mistakes in Section

Intestinal microbial communities of rainbow trout (Oncorhynchus mykiss) may be improved by feeding a Hermetia illucens meal/low-fishmeal diet.

With demands and reliance on aquaculture still growing, there are various challenges to allow sustainable growth and the shift from fishmeal (FM) to other protein sources in aquafeed formulations is one of the most important. In this regard, interest in the use of insect meal (IM) in aquafeeds has grown rapidly. Accordingly, the aim of the present study was to assess the effects of dietary IM from Hermetia illucens (Hi) larvae included in a low-FM diet on gut microbial communities of rainbow trout (Oncorhynchus mykiss), in terms of both composition and function of microbiome. A feeding trial was conducted using 192 trout of about 100-g mean initial weight. Fish were fed in quadruplicate (4 tanks/diet) for 131 days with two diets: the control (Ctrl) contained 20% of FM as well as other protein sources, whereas the Hi diet contained 15% of Hi larvae meal to replace 50% of the FM contained in the Ctrl diet. High-throughput sequencing of 16S rRNA gene was used to identify the major feed and gut bacterial taxa, whereas Phylogenetic Investigation of Communities by Reconstruction of Unobserved States (PICRUSt) analysis was performed on gut bacterial genomes to identify the major active biological pathways. The inclusion of IM led to an increase in Firmicutes, mainly represented by Bacilli class and to a drastic reduction of Proteobacteria. Beneficial genera, such as Lactobacillus and Bacillus, were enriched in the gut of fish fed with the Hi diet, whereas the number of bacteria assigned to the pathogenic Aeromonas genus was drastically reduced in the same fish group. The metagenome functional data provided evidence that dietary IM inclusion can shape the metabolic activity of trout gut microbiota. In particular, intestinal microbiome of fish fed with IM may have the capacity to improve dietary carbohydrate utilization. Therefore, H. illucens meal is a promising protein source for trout nutrition, able to modulate gut microbial community by increasing the abundance of some bacteria taxa that are likely to play a key role in fish health

Control of spatiotemporal rogue waves by harmonic pump modulation in a semiconductor laser with a saturable absorber

Through numerical simulations, statistical and dynamical properties of extreme events in a broad-area semiconductor laser with intracavity saturable absorber are investigated. By inclusion of a diffusion coefficient for the field, formation of rogue waves in a state of extended turbulence is studied and shown to be affected by harmonic perturbations. In particular, we propose a control technique based on periodic modulation of the pump parameter which can either drive the state of the system closer to or away from the chaotic attractors respectively enhancing or suppressing the generation of rogue waves. By statistical and dynamical analysis of the events in terms of intensity and optical gain, we show that when the system is under resonant modulation with frequency close to that of the dominant oscillations in the turbulent state (which is equal to the relaxation oscillation frequency typical of semiconductor lasers), more rogue waves are triggered with larger intensities and shorter lifetimes. On the other hand, off-resonant modulations restrain the formation of rogue waves where they appear in lower intensities and longer lifetimes. An example of special cases where the proposed scheme can completely forbid or allow the emission of rogue waves is also presented

Exploiting coordination geometry to selectively predict the r-donor and p-acceptor abilities of ligands: a back-and-forth journey between electronic properties and spectroscopy

Coordination geometry switches the carbonyl stretching frequency into a selective probe of the σ-donor and π-acceptor abilities of ligands

Asymmetric Hydrogenation of 1-aryl substituted-3,4-Dihydroisoquinolines with Iridium Catalysts Bearing Different Phosphorus-Based Ligands

Starting from the chiral 5,6,7,8-tetrahydroquinolin-8-ol core, a series of amino-phosphorusbased ligands was realized. The so-obtained amino-phosphine ligand (L1), amino-phosphinite (L2) and amino-phosphite (L3) were evaluated in iridium complexes together with the heterobiaryl diphosphines tetraMe-BITIOP (L4), Diophep (L5) and L6 and L7 ligands, characterized by mixed chirality. Their catalytic performance in the asymmetric hydrogenation (AH) of the model substrate 6,7-dimethoxy-1-phenyl-3,4-dihydroisoquinoline 1a led us to identify Ir-L4 and Ir-L5 catalysts as the most eective. The application of these catalytic systems to a library of dierently substituted 1-aryl-3,4-dihydroisoquinolines aorded the corresponding products with variable enantioselective levels. The 4-nitrophenyl derivative 3b was obtained in a complete conversion and with an excellent 94% e.e. using Ir-L4, and a good 76% e.e. was achieved in the reduction of 2-nitrophenyl derivative 6a using Ir-L5

Dynamic regimes and damping of relaxation oscillations in III-V/Si external cavity lasers

We report how external cavity IIIV/Si hybrid lasers operate in regimes of ultradamped relaxation oscillations or in turbulent and selfpulsing regimes. The different regimes are reached by detuning the lasing wavelength respect to the mirror effective reflectivity peak and are the consequence of the dispersive narrow band reflectivity of the silicon photonics mirror, the linewidth enhancement factor and fourwave mixing in the gain medium