The primary purpose of this research article is to study the famous K$\ddot{o}$the's Conjecture for the special cases - when a ring $\mathfrak{R}$ is commutative, and when $\mathfrak{R}$ is an Algebra over a field. Furthermore, some open problems involving tensor product of Algebras over a field has also been discussed extensively along with their proofs. Subsequently, an equivelent statement of K$\ddot{o}$the's problem in terms of algebra of matrices has been established.

Supplementation with 200% of the recommended daily dietary quantity of copper modified vascular contraction and relaxation through increased reactive oxygen species (ROS) and prostaglandin formation, which modified the antioxidant status of middle–aged rats. In this study, young (1 month old) male Wistar rats (n/group = 10) received a diet supplemented with 6.45 mg copper/kg (100%—Group A) for 8 weeks. The experimental group received 12.9 mg copper/kg of diet (200%—Group B). Experimental supplementation with 200% copper increased the copper concentration in the blood, liver, and kidneys; increased the ROS concentration in the aortic rings; and enhanced the sensitivity of the aortic rings to acetylcholine. We observed increased participation of nitric oxide (NO) derived from inducible NO synthase (iNOS) in vascular contraction and a decreased net effect of vasodilator prostanoids derived from cyclooxygenase–2 (COX–2) in vascular relaxation. Supplementation with 200% copper was less significant than expected after previous studies conducted with middle–aged rats.

We give three new systematic authentication schemes, two using Gray map, finite fields and Galois rings, and one using only Galois rings. In the first scheme, we increase the size and simplify the scheme’s source space in [9]. In the second scheme, we reduce the key space of the first scheme. Finally, by not considering Gray map, used in the previous schemes, we give a third scheme on Galois rings, which generalizes the scheme over finite fields given in [8]. The introduced schemes obtain optimal impersonation and substitution probabilities.

Purpose: This pilot ex-vivo study and first clinical experience in Italy evaluate the impact of using pre-implantation crosslinking on all-femtosecond laser-cut corneal allogenic intracorneal ring segments (AFXL CAIRS). Methods: Six human donor eye-bank corneas were used for the preclinical ex-vivo human study. Three corneas were used for AFXL CAIRS. First, they were prepared (D) with the IntraLase™ femtosecond laser (Johnson & Johnson, USA). The allogenic tissue rings were crosslinked before implantation with Riboflavin -UV-A accelerated crosslinking protocol (ACXL) with a 0.1% HPMC Riboflavin isotonic solution (Vibex Rapid, Glaukos-Avedro, USA) and the new KXL UV-A emitter (Glaukos-Avedro, USA). Three corneas were used as recipients (R) of the AFXL CAIRS. After completing the ex-vivo phase, the first two Italian patients were treated. A single ACXL CAIRS was implanted in a 51-year-old male with 53.53 D K steep, 363 m minimum corneal thickness (MCT) and a double ACXL CAIRS was implanted in a 46-year-old male patient with 58.30 D K steep and 443 m MCT. The follow-up was at three months. Results: Crosslinking of the segments enhanced tissue strength and grip, facilitating manipulation and CAIRS insertion into the recipient tunnels and the yellowish color of the crosslinked segments improved visibility. The segment’s thickness and volume remained unaltered during the follow-up. Both patients improved UDVA and BSCVA. K steep and HOAs were reduced and MCT increased. Conclusions Pre-implantation ACXL facilitated CAIRS insertion by increasing the viscoelastic consistency without altering physical characteristics and volume during the follow-up, rendering this important step a promising candidate in method standardization. Functional data and MCT improved significantly without adverse events.

In this article some important observations have been reported on recent works related to weakly tripotent rings and locally invo-regular rings. Our findings give additional results as well as correct some recent results on weakly tripotent rings and locally invo-regular rings appeared in Rendiconti Sem. Mat. Univ. Pol. Torino (2021) and Azerbaijan Journal of Mathematics (2021) respectively.

A plasmonic refractive index (RI) sensor based on metal-insulator-metal (MIM) waveguide coupled with concentric double rings resonator (CDRR) is proposed and investigated numerically. Utilizing the novel supermodes of the CDRR, the FWHM of the resonant wavelength can be modulated, and a sensitivity of 1060 nm/RIU with high figure of merit (FOM) 203.8 is realized in the near-infrared region. The unordinary modes as well as the influence of structure parameters on the sensing performance are also discussed. Such plasmonic sensor with simple framework and high optical resolution could be applied to on-chip sensing systems and integrated optical circuits. Besides, the special cases of bio- sensing and triple rings are also discussed.

This study investigates the vertical structure of the dynamical properties of a warm-core ring in the Gulf of Mexico (Loop Current ring) using glider observations. We introduce a new method to correct the glider’s along-track coordinate which is, in general, biased by the unsteady relative movements of the glider and the eddy, yielding large errors on horizontal derivatives. Here, we take advantage of the synopticity of satellite along-track altimetry to apply corrections on the glider’s position, by matching in situ steric height with satellite-measured sea surface height. This relocation method allows to recover the eddy’s azimuthal symmetry, to precisely estimate the rotation axis position, and to compute reliable horizontal derivatives. It is shown to be particularly appropriate to compute the eddy’s cyclo-geostrophic velocity, relative vorticity, and shear strain, which are otherwise out of reach when using the glider’s raw traveled distance as an horizontal coordinate. The Ertel potential vorticity (PV) structure of the warm core ring is studied in details, and we show that the PV anomaly is entirely controlled by vortex stretching. Sign reversal of the PV gradient across the water column suggests that the ring might be baroclinically unstable. The PV gradient is also largely controlled by gradients of the vortex stretching term. We also show that the ring’s total energy partition is strongly skewed, with available potential energy being 3 times larger than kinetic energy. The possible impact of this energy distribution on the Loop Current rings longevity is also discussed.

Paleoclimate information is key to understanding the climate system and predicting future climate. Currently, stable isotope analysis of whole molecules in tree rings is among the most advanced paleoclimate tools. Still, it only enables reconstructions of one climate parameter at a time (univariate climate reconstruction), a fundamental limitation. Here, we investigated whether this limitation can be overcome by analysing isotope variability at the level of intramolecular carbon positions in tree-ring glucose. We found that drought governs isotope variability at glucose C-1 to C-3, whereas radiation governs isotope variability at glucose C-5 to C-6. These isotope-climate relationships are statistically and mechanistically robust. According to cross-validation analysis, they can be reconstructed with high accuracy and precision. Thus, intramolecular isotope analysis enables multivariate climate reconstructions (proof of concept).

The three-dimensional structure of Gulf of Mexico’s warm-core rings, detaching from the Loop Current, is investigated using satellite altimetry and a large set of ARGO float profiles. Reconstruction of the Loop Current rings (LCRs) vertical structure from sea surface height observations is made possible by the use of the gravest empirical modes method (GEM). The GEMs are transfer functions that associate a value of temperature and salinity for each variable pair {dynamic height;pressure}, and are computed by estimating an empirical relationship between dynamic height and the vertical thermohaline structure of the ocean. Between 1993 and 2021, 40 LCRs were detected in the altimetry and their three-dimensional thermohaline structure was reconstructed, as well as a number of dynamically relevant variables (geostrophic and cyclogeostrophic velocity, relative vorticity, potential vorticity, available potential energy and kinetic energy density etc.). The structure of a typical LCR was computed by fitting an analytical stream function to the LCRs dynamic height signature and reconstructing its vertical structure with the GEM. The total heat and salt contents and energy of each LCR were computed and their cumulative effect on the Gulf of Mexico’s heat, salt and energy balance is discussed. We show that LCRs have a dramatic impact on these balances and estimate that residual surface heat fluxes of -13 Wm−2 are necessary to compensate their heat input, while the fresh water outflow of the Mississippi river approximately compensates for their salt excess input. An average energy dissipation of O[10−10−10−9] Wkg−1 would be necessary to balance their energy input.

Long-acting (LA) drug-delivery system (DDS) successes are linked to their abilities to harness biocompatible polymers and materials for sustained and predictable release of therapeutic agents over an extended period of time. For human immune deficiency virus type one (HIV-1) infections, LA DDSs hold great promise in closing the gaps of daily oral therapy for treatment and prevention. Examples are Cabenuva, Apretude and Sunlenca, which have been shown to be safe and effective. Alternative promising drug delivery technologies such as implants, prodrugs, vaginal rings, and microarray patches are being explored to further meet patients’ needs. We posit that improved physicochemical properties of the formulation payloads and material chemistry design with optimal drug release kinetics holds the potential to optimize release profiles. Furthermore, for the treatment and prevention of HIV-1 infection, the landscape of LA medicines now in clinical or preclinical development offers hope that the strategic design of polymers will further improve upon controlled delivery of drugs to simplify dosing schedules.

The dependence of the width of annual rings of woody plants on the characteristics of the snow cover is analyzed in various natural zones of the West Siberian Plain and adjacent mountainous areas: the maximum thickness and water reserve for the entire winter period and for individual months, the dates of disappearing, establishment, and duration of the occurrence of a stable snow cover. It has been shown that the role of the thickness and water content of snow cover for the radial growth of trees is differentiated by geographical location. On the plain, it intensifies in the forest-tundra and dry steppe. The response of radial growth to snow cover in the upper and lower parts of the forest belt is often opposite. Dates of establishment of stable snow cover are more important for tree growth compared to dates of disappearance. Dates of disappearance of stable snow cover are more significant in the southern regions than in the northern ones. The value of the duration of the period with stable snow cover for tree growth is higher in the southern regions.

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z^(-1) which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z^(- i) by time functions which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of z^(i) at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

Structure and reversibility of cross-link junctions play pivotal roles in deter- mining the nature of thermoreversible gelation and dynamic mechanical prop- erties of the produced polymer networks. We attempt to explore new types of sol–gel transitions with mechanical sharpness by allowing cross-links to grow without upper bound. We consider thermoreversible gelation of the primary molecules R{Af} carrying the number f of low molecular weight functional groups (gelators) A. Gelators A are assumed to form supramolecular assemblies. Some examples are: telechelic polymers (f = 2) carrying π–π stacking benzene derivatives at their both ends, trifunctional star molecules (f = 3) bearing mul- tiple hydrogen-bonding gelators. The sol–gel transition of the primary molecules becomes sharper with the cooperativity parameter of the stepwise linear growth of the cross-links. There is a polymerization transition (crossover without singu- larity) of the junctions in the postgel region after the gel point is passed. If the gelator A tends to form supramolecular rings competitively with linear chains, there is another phase transition in the deep postgel region where the average molecular weight of the rings becomes infinite (Bose-Einstein condensation of rings). As a typical example of binary cross-links where gelators A and B form mixed junctions, we specifically consider metal-coordinated binding of ligands A by metal ions B. Two types of multi-nuclear supramolecular complexes are studied: (i) linear stacking (ladder) of the sandwich A2B units, (ii) linear train of egg-box A4B units. The average molecular weight, the gel fraction, the av- erage length of the cross-link junctions are calculated for all of these models as functions of the functionality f, the concentration of the solute molecules, and temperature. Potential candidates for the realization of these new types of thermoreversible gelation are discussed.

This paper analyses the viability of different solutions to passively augment the axial stiffness of a horizontal axis radial levitation passive magnetic bearing (PMB) with topology previously studied. The zero-field cooling (ZFC) of high-temperature superconductor (HTS) bulks promotes higher magnetic impulsion and levitation forces and lower electromagnetic losses than with the field-cooling (FC), but on the other hand, the guiding stability is much lower than with FC. Because of stability reasons, FC was adopted in most superconducting maglev systems. The trend of this research group has been to develop an HTS ZFC horizontal axis radial levitation PMB presenting notable levitation forces with reduced electromagnetic losses, defined by a topology that creates guiding stability. Previous work has shown that even optimizing the bearing geometry to maximize magnetic guidance forces, could not be enough to guarantee the axial stiffness required for many applications. First, the extent to which guidance forces are augmented by increasing the number of HTS bulks in the stator is evaluated. Then, the axial stiffness augmentation by passively adding two limiting permanent magnet (PM) rings is evaluated. Results show that the axial stiffness is highly augmented by adding limiting PM rings with no significant additional investment. This change enables using the studied ZFC superconducting PMB in high-precision axial stability applications, such as precision gyroscopes, horizontal axis propellers and turbines.

This paper extends the application of the ROTASE model for the formation of spiral arms of disc galaxies, questions and confusions from readers about this model are addressed. The optical trail effect behind the spiral arm rotation is the natural consequence of the model. The morphologies of ring-galaxies are classified into four categories: type I: single ring; type II: 8-shaped double ring; type III: 8-shaped double ring wrapped by a larger outer ring; type IV: single ring without spiral and bar. All four types of ring galaxies can be described by the ROTASE model. The ROTASE model predicts that the false impression of spiral arm rotating ahead of the galactic bar in the galaxy MCG+00-04-051 will change with time, it will look like a normal galaxy with about 30° to 40° bar rotation in the future and the galactic bar ends will look like rotating ahead of the spiral arms with further 10 ° to 15 °bar rotation. The formation of one arm galaxies is due to X-matter at one side of supermassive black hole is much stronger than other side. More evidence is found to support the explanation of the formation and the evolution of the Hoag’s object. The possible evolution of spiral pattern of galaxies is illustrated by UGC 6093. The winding of the Milky Way could be tighter in the future based on the ROTASE model.

Retrospective information about the climate system and plant ecophysiology are key inputs in climate and Earth system modelling. Dendrochronology provides such information with large spatiotemporal coverage, and stable carbon isotope (¹³C/¹²C) analysis across tree-ring series is among the most advanced dendrochronological tools. For the past seventy years, this analysis was performed on whole molecules, and, to this day, ¹³C/¹²C variation is attributed to ¹³C discrimination during CO₂ diffusion into leaves and assimilation by rubisco. By contrast, ¹³C discrimination by post-rubisco processes is presumed constant. Here, recently reported results on the first dataset of intramolecular ¹³C discrimination in tree rings were synthesised by variance component analysis. The emerging picture is not consistent with the classical (DR-discrimination-centred) concepts and practices of carbon-isotope dendrochronology. Specifically, leaf and stem post-rubisco discrimination each account for more variation in the data than diffusion-rubisco discrimination, i.e., post-rubisco discrimination is not constant. Furthermore, diffusion-rubisco discrimination is used widely as proxy of leaf intrinsic water-use efficiency (iWUE), a key determinant in the responses of global biogeochemical cycles to climate change. However, since diffusion-rubisco discrimination is a small component of the total data variance, whole-molecule analysis yields confounded iWUE estimates, yet intramolecular analysis will likely offer solutions. Lastly, all currently observed ¹³C/¹²C-climate relationships are attributed to diffusion-rubisco discrimination. However, here, relationships with temperature and radiation derive from leaf-level post-rubisco discrimination while relationships with precipitation derive from stem-level post-rubisco discrimination. That said, advances in mass spectrometry may soon make intramolecular ¹³C/¹²C analysis broadly available taking carbon-isotope dendrochronology to the next level.