Results on the Projective Plane over a Finite Field of Order Seventeen

The main goal of this research is to find the projective mapping that transforms a geometric formation called an i -set onto an arc such that the domain of the mapping is a subset of the projective line PG (1,q), q=17 , such that a5-set is called a pentad, a6-set is a hexad, a7-set is a heptad, a8-set is an octad, and a9 -set is a nonad, mapped onto a conicY2-XZ. The research also aims to find the stabilizer group of points on a non-singular cubic curve, with or without rational inflection points, on the projective plane over a finite field of order seventeen, and to give some examples.

Strong shift equivalence and algebraic K-theory

For a semiring \mathcal{R} , the relations of shift equivalence over \mathcal{R} ( \textup{SE-}\mathcal{R} ) and strong shift equivalence over \mathcal{R} ( \textup{SSE-}\mathcal{R} ) are natural equivalence relations on square matrices over \mathcal{R} , important for symbolic dynamics. When \mathcal{R} is a ring, we prove that the refinement of \textup{SE-}\mathcal{R} by \textup{SSE-}\mathcal{R} , in the \textup{SE-}\mathcal{R} class of a matrix A, is classified by the quotient NK_{1}(\mathcal{R})/E(A,\mathcal{R}) of the algebraic K-theory group NK_{1}(\mathcal{R}) . Here, E(A,\mathcal{R}) is a certain stabilizer group, which we prove must vanish if A is nilpotent or invertible. For this, we first show for any square matrix A over \mathcal{R} that the refinement of its \textup{SE-}\mathcal{R} class into \textup{SSE-}\mathcal{R} classes corresponds precisely to the refinement of the \mathrm{GL}(\mathcal{R}[t]) equivalence class of I-tA into \mathrm{El}(\mathcal{R}[t]) equivalence classes. We then show this refinement is in bijective correspondence with NK_{1}(\mathcal{R})/E(A,\mathcal{R}) . For a general ring \mathcal{R} and A invertible, the proof that E(A,\mathcal{R}) is trivial rests on a theorem of Neeman and Ranicki on the K-theory of noncommutative localizations. For \mathcal{R} commutative, we show \cup_{A}E(A,\mathcal{R})=NSK_{1}(\mathcal{R}) ; the proof rests on Nenashev’s presentation of K_{1} of an exact category.

Influence of a Capping Ligand on the Band Gap and Excitonic Levels in Colloidal Solutions and Films of ZnSe Quantum Dots

Semiconductor quantum dots are promising nanostructures for their application in solar cells of the 3rd generation, photodetectors, light emitting diodes, and as biological markers. However, the issue concerning the influence of superficial organic stabilizers (ligands) on the energy of excitons in quantum dots still remains open. In this work, by analyzing the optical spectra of colloidal solutions and films of ZnSe quantum dots stabilized with 1-thioglycerol, it is found that the energy of excitons and their migration depend not only on the quantum confinement effect, but also on the superficial contribution from the thiol stabilizer group –SH. The dependence of the exciton energy in ZnSe quantum dots on the surface stabilizer concentration is experimentally revealed for the first time. The short size of the stabilizer molecular chain and the large initial energy of excitons are shown to result in the effective migration of excitons over an array of quantum dots.

Partitions on Finite Projective Lines

The goal of this paper is to split the finite projective line into disjoint sublines by method of subgeometries where the order of line is not a prime number. The correspondence between the points on a line and the points on a conic has been described. The stabilizer group of some lines has been constructed using the fundamental theory of projective lines. All calculations are done using the GAP program. Also primitive polynomials over Galois filed are classified. Some examples with groups which are the fixed points of lines and study the properties of these groups are introduced. The nonsingular matrices which generate the points of conic and belong to groups of projectivities have been constructed.

Atypical Antipsychotics and the Human Skeletal Muscle Lipidome

Atypical antipsychotics (AAPs) are a class of medications associated with significant metabolic side effects, including insulin resistance. The aim of this study was to analyze the skeletal muscle lipidome of patients on AAPs, compared to mood stabilizers, to further understand the molecular changes underlying AAP treatment and side effects. Bipolar patients on AAPs or mood stabilizers underwent a fasting muscle biopsy and assessment of insulin sensitivity. A lipidomic analysis of total fatty acids (TFAs), phosphatidylcholines (PCs) and ceramides (CERs) was performed on the muscle biopsies, then lipid species were compared between treatment groups, and correlation analyses were performed with insulin sensitivity. TFAs and PCs were decreased and CERs were increased in the AAP group relative to those in the mood stabilizer group (FDR q-value <0.05). A larger number of TFAs and PCs were positively correlated with insulin sensitivity in the AAP group compared to those in the mood stabilizer group. In contrast, a larger number of CERs were negatively correlated with insulin sensitivity in the AAP group compared to that in the mood stabilizer group. The findings here suggest that AAPs are associated with changes in the lipid profiles of human skeletal muscle when compared to mood stabilizers and that these changes correlate with insulin sensitivity.

Automorphism groups and invariant theory on ℙN

Let [Formula: see text] be a field and [Formula: see text] a morphism. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group [Formula: see text]. The group of automorphisms, or stabilizer group, of a given [Formula: see text] for this action is known to be a finite group. In this paper, we apply methods of invariant theory to automorphism groups by addressing two mainly computational problems. First, given a finite subgroup of [Formula: see text], determine endomorphisms of [Formula: see text] with that group as a subgroup of its automorphism group. In particular, we show that every finite subgroup occurs infinitely often and discuss some associated rationality problems. Inversely, given an endomorphism, determine its automorphism group. In particular, we extend the Faber–Manes–Viray fixed-point algorithm for [Formula: see text] to endomorphisms of [Formula: see text]. A key component is an explicit bound on the size of the automorphism group depending on the degree of the endomorphism.

The key role of microtubules in hypoxia preconditioning-induced nuclear translocation of HIF-1α in rat cardiomyocytes

Background Hypoxia-inducible factor (HIF)-1 is involved in the regulation of hypoxic preconditioning in cardiomyocytes. Under hypoxic conditions, HIF-1α accumulates and is translocated to the nucleus, where it forms an active complex with HIF-1β and activates transcription of approximately 60 kinds of hypoxia-adaptive genes. Microtubules are hollow tubular structures in the cell that maintain cellular morphology and that transport substances. This study attempted to clarify the role of microtubule structure in the endonuclear aggregation of HIF-1α following hypoxic preconditioning of cardiomyocytes. Methods Primary rat cardiomyocytes were isolated and cultured. The cardiomyocyte culture system was used to establish a hypoxia model and a hypoxic preconditioning model. Interventions were performed on primary cardiomyocytes using a microtubule-depolymerizing agent and different concentrations of a microtubule stabilizer. The microtubule structure and the degree of HIF-1α nuclear aggregation were observed by confocal laser scanning microscopy. The expression of HIF-1α in the cytoplasm and nucleus was detected using Western blotting. Cardiomyocyte energy content, reflected by adenosine triphosphate/adenosine diphosphate (ATP/ADP), and key glycolytic enzymes were monitored by colorimetry and high-performance liquid chromatography (HPLC). Reactive oxygen species (ROS) production was also used to comprehensively assess whether microtubule stabilization can enhance the myocardial protective effect of hypoxic preconditioning. Results During prolonged hypoxia, it was found that the destruction of the microtubule network structure of cardiomyocytes was gradually aggravated. After this preconditioning, an abundance of HIF-1α was clustered in the nucleus. When the microtubules were depolymerized and hypoxia pretreatment was performed, HIF-1α clustering occurred around the nucleus, and HIF-1α nuclear expression was low. The levels of key glycolytic enzymes were significantly higher in the microtubule stabilizer group than in the hypoxia group. Additionally, the levels of lactate dehydrogenase and ROS were significantly lower in the microtubule stabilizer group than in the hypoxia group. Conclusion The microtubules of cardiomyocytes may be involved in the process of HIF-1α endonuclear aggregation, helping to enhance the anti-hypoxic ability of cardiomyocytes.

Stabilizer codes and equientangled bases from phase states

We develop a comprehensive approach of stabilizer codes and provide a scheme generating equientangled basis interpolating between the product basis and maximally entangled basis. The key ingredient is the theory of phase states for finite-dimensional systems (qudits). In this respect, we derive entangled phase states for a multiqudit system whose dynamics is governed by a two-qudit interaction Hamiltonian. We construct the stabilizer codes for this family of entangled phase states. The stabilizer phase states are defined as the common eigenvectors of the stabilizer group generators which are explicitly specified. Furthermore, we construct equally entangled bases from bipartite as well as multipartite entangled qudit phase states.

Picard groups of higher real -theory spectra at height

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real $K$-theory spectra of Hopkins and Miller at height $n=p-1$, for $p$ an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra $E_{n}^{hG}$, where $E_{n}$ is Lubin–Tate $E$-theory at the prime $p$ and height $n=p-1$, and $G$ is any finite subgroup of the extended Morava stabilizer group. We find that these Picard groups are always cyclic, generated by the suspension.