Doubling Of Number Research Articles

Lagrange's mean value theorem in hyperbolic number plane

Hyperbolic number is a generalization of real number, it is a commutative ring of zero factor, and has been widely used in many fields such as mathematics, physics and engineering. In this paper, we first review the basic concepts and properties of hyperbolic numbers, and then study the Lagrange's mean value theorem on the hyperbolic numbers plane, and get a more general theorem. This not only provides impetus for the development of hyperbolic analysis, but also further injects energy into the development of applied mathematics.

Accelerated charging dynamics in shell-and-multi-tube latent heat storage systems for building applications

Thermal energy storage (TES) is an emerging technique to store the surplus energy generated during periods of excess supply and utilise it when demand arises. Phase change material (PCM) stands out as a highly efficient TES system. Enhancing heat transfer during phase change is a major challenge in creating effective PCM-based TES systems. This study focuses on enhancing the melting performance of a shell-and-tube latent heat thermal energy storage (LHTES) system. This improvement is achieved by conducting an extensive parametric study involving various geometric factors including tube position from the bottom, vertical tube spacing, tube diameter, different heat exchanger shell aspect ratios, PCM temperature, tube temperature, and PCM type. A three-dimensional model is simplified to a two-dimensional geometry for numerical simulation. The results indicate that the PCM melting time decreased by 20.6 % and 4.4 % with a 20 mm vertical tube distance compared to 15 mm and 25 mm. Among the considered scenarios, the configuration with a doubled number of tubes in width consistently exhibits a higher melt fraction throughout the entire duration. Regarding the aspect ratio, the square-shaped system demonstrates both quicker melting times and a higher energy storage rate. When comparing PCM types, it is evident that RT 35 exhibits a 3.2 % higher heat storage rate and a 44.7 % shorter melting time compared to RT 35 HC.

Tensile properties of unidirectional thermosetting composites reinforced with ring-spun hybrid yarns including recycled carbon fiber

The study of composites reinforced with aligned recycled carbon fiber (CF) is gaining increasing attention, particularly in light of the circular economy. Hybrid yarns, among other oriented reinforcements, have gained interest from researchers who have already utilized them to produce unidirectional thermoplastic composites. Nevertheless, the evaluation of unidirectional thermosetting composites reinforced with hybrid yarns is still lacking. This article presents their production, leveraging a recently developed process, and mechanical characterization. The results show that the amount of recycled CF and the number of draw frame doublings within the hybrid yarns affect the tensile properties of the composite, while the thermoplastic fiber has no influence, as also suggested by the main effect plots. Two-way interactions exhibit different behaviors depending on the tensile property considered. Overall, the composite material with the best tensile properties was that reinforced with a ring-spun hybrid yarn consisting of 70% recycled CF, 30% polyamide, and five draw frame doublings.

Minimal timelike surfaces in the Lorentz–Minkowski 3-space and their canonical parameters

We study minimal timelike surfaces in \(\mathbb R^3_1\) using a special Weierstrass-type formula in terms of holomorphic functions defined in the algebra of the double (split-complex) numbers. We present a method of obtaining an equation of a minimal timelike surface in terms of canonical parameters, which play a role similar to the role of the natural parameters of curves in \(\mathbb R^3\). Having one holomorphic function that generates a minimal timelike surface, we find all holomorphic functions that generate the same surface. In this way we give a correspondence between a minimal timelike surface and a class of holomorphic functions. As an application, we prove that the Enneper surfaces are the only minimal timelike surfaces in \(\mathbb R^3_1\) with polynomial parametrization of degree 3 in isothermal parameters.

Dual quaternion theory over HGC numbers

Knowing the applications of quaternions in various fields, such as robotics, navigation, computer visualization and animation, in this study, we give the theory of dual quaternions considering Hyperbolic-Generalized Complex (HGC) numbers as coefficients via generalized complex and hyperbolic numbers. We account for how HGC number theory can extend dual quaternions to HGC dual quaternions. Some related theoretical results with HGC Fibonacci/Lucas numbers are established, including their dual quaternions. Given HGC Fibonacci/Lucas numbers, their special matrix correspondences have been identified and these are carried out to HGC Fibonacci/Lucas dual quaternions. Furthermore, we provide a more accurate way to quickly calculate HGC Fibonacci numbers and associate this with HGC generalized Fibonacci numbers. For implementation, we produce an algorithm in Maple. Lastly, we put the theory into practice.

Double Total Domination Number on Some Chemical Nanotubes

Suppose G is a graph with the vertex set V (G). A set D ⊆ V (G) is a total k-dominating set if every vertex v ∈ V (G) has at least k neighbours in D. The total k-domination number γkt(G) is the size of the smallest total k-dominating set. When k = 2 the total 2-dominating set is referred to as a double total dominating set. In this work we compute the exact values for double total domination number on H-phenylenic nanotubes HPH(m,n), m,n ≥ 2 and H-naphtalenic nanotubes HN(m,n), n = 2k, m,n ≥ 2. As all vertices have a degree 2 or 3, there is no total k-domination for k ≥ 3 for H-phenylenic and H-naphtalenic nanotubes, and the double total domination is the maximum possible.

The Squeeze Principle of the Sequence of Hyperbolic Numbers

The Squeeze Principle of the Sequence of Hyperbolic Numbers

On some Combinatorial Properties of Generalized Commutative Pell and Pell-Lucas Quaternions

Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we study generalized commutative Pell quaternions and generalized commutative Pell-Lucas quaternions. We present some properties of these numbers and relations between them.

Efficacy of axillary dead space closure after mastectomy, axillary clearance and prosthetic reconstruction: a single-center preliminary experience.

Postoperative seroma is most frequent after mastectomy (ME) in combination with axillary lymph node dissection (ALND), and its reported incidence varies from 15.5% up to 90%. Seromas can be responsible for discomfort, infections and can lead to reconstruction failure. Therefore, many ways of seroma prevention have been studied, although from a recent overview it has become clear that no single method is reliably successful. Mechanical closure of the dead space, however, was consistently found to be significantly effective. The aim of our study is to evaluate if quilting of the axilla, in patients undergoing ME, immediate prosthetic breast reconstruction and ALND reduces the duration of drain maintenance, the incidence of seromas that require aspiration (clinically significant seromas, CSS) and reconstruction failure rate. In our study population we analyzed a total of 81 patients divided into two groups: 27 consecutive patients undergoing mastectomy, axillary lymph node dissection (ALND), breast reconstruction and quilting of the axilla. We subsequently randomly picked up a double number of patients (54) undergoing the same oncological and reconstructive procedures without undergoing axillary quilting, matched for clinical characteristics in order to analyze efficacy of the procedure while reducing any bias. Our observational retrospective data was collected from October 2016 to July 2020 in one single high-volume center. Our median follow-up time was of 40.6 months. In the case group we observed a reduced time of drain maintenance: 16 vs. 20 days observed in the non-quilted group (p < 0.05). Incidence of seromas that required aspiration was 11% in the control group, while 3,7% in the case group. In addition to that, we observed 6 cases of implant removal in the control group, while in the quilted group we only observed a single case. Previous literature and our results confirm that quilting of the axilla with flap fixation significantly decreases time of drain maintenance, allowing the earlier removal of the drains as well as decreasing the incidence of seroma, its eventual associated complications and related social costs. Moreover, our work suggests how quilting sutures decrease the incidence of seroma in patients undergoing immediate reconstruction, probably reducing the risk for implant removal.

Acute myocardial infarction preferentially alters low-abundant, long-chain unsaturated phospholipid and sphingolipid species in plasma high-density lipoprotein subpopulations

AimHigh-density lipoprotein (HDL) particles in ST-segment elevation myocardial infarction (STEMI) are deficient in their anti-atherogenic function. Molecular determinants of such deficiency remain obscure. MethodsFive major HDL subpopulations were isolated using density-gradient ultracentrifugation from STEMI patients (n = 12) and healthy age- and sex-matched controls (n = 12), and 160 species of phosphatidylcholine, lysophosphatidylcholine, phosphatidylethanolamine, phosphatidylinositol, phosphatidylglycerol, phosphatidylserine, phosphatidic acid, sphingomyelin and ceramide were quantified by LC-MS/MS. ResultsMultiple minor species of proinflammatory phosphatidic acid and lysophosphatidylcholine were enriched by 1.7–27.2-fold throughout the majority of HDL subpopulations in STEMI. In contrast, minor phosphatidylcholine, phosphatidylglycerol, phosphatidylinositol, phosphatidylethanolamine, sphingomyelin and ceramide species were typically depleted up to 3-fold in STEMI vs. control HDLs, while abundances of their major species did not differ between the groups. Intermediate-to-long-chain phosphatidylcholine, phosphatidylinositol and phosphatidylglycerol species were more affected by STEMI than their short-chain counterparts, resulting in positive correlations between their fold decrease and the carbon chain length. Additionally, fold decreases in the abundances of multiple lipid species were positively correlated with the double bond number in their carbon chains. Finally, abundances of several phospholipid and ceramide species were positively correlated with cholesterol efflux capacity and antioxidative activity of HDL subpopulations, both reduced in STEMI vs controls. KEGG pathway analysis tied these species to altered glycerophospholipid and linoleic acid metabolism. ConclusionsMinor unsaturated intermediate-to-long-chain phospholipid and sphingolipid species in HDL subpopulations are most affected by STEMI, reflecting alterations in glycerophospholipid and linoleic acid metabolism with the accumulation of proinflammatory lysolipids and maintenance of homeostasis of major phospholipid species.

Performance analysis and optimization of frequency division duplex based virtual full-duplex communication systems

Virtual full-duplex (VFD) communication systems have become smart alternative over residual self-interference (RSI) affected full-duplex (FD) systems and thus has drawn significant research attention in the recent years. However, in comparison to FD, the VFD system models studied in the literature are based on successive relaying (SR) that require an extra time phase and a double number of relays for each destination user. Thus, we propose a novel frequency division duplex (FDD) based VFD (FDD-VFD) system model that can not only match FD in terms of resource utilization but also outperform both SR-VFD and FD. We consider two practical scenarios of absence of inter relay interference (A-IRI) and presence of IRI (P-IRI). We analyze the outage probability and ergodic rate performance metrics and present their analytical expressions in closed-form over Nakagami-m fading channels. Next, to minimize the effect of inter-relay interference in P-IRI scenario, we investigate optimization problems of minimizing the system outage probability and maximizing the ergodic sum rate for jointly allocating transmit power of the relays. We utilize particle swarm optimization algorithm and deep learning architecture to solve the formulated problems. Extensive evaluations are carried out over different system parameters to prove the efficacy of proposed FDD scheme and obtain key inferences.

Asymptotics for real monotone double Hurwitz numbers

In recent years, monotone double Hurwitz numbers were introduced as a naturally combinatorial modification of double Hurwitz numbers. Monotone double Hurwitz numbers share many structural properties with their classical counterparts, such as piecewise polynomiality, while the quantitative properties of these two numbers are quite different. We consider real analogues of monotone double Hurwitz numbers and study the asymptotics for these real analogues. The key ingredient is an interpretation of real tropical covers with arbitrary splittings as factorizations in the symmetric group which generalizes the result from Guay-Paquet et al. (2016) [18]. By using the above interpretation, we consider three types of real analogues of monotone double Hurwitz numbers: real monotone double Hurwitz numbers relative to simple splittings, relative to arbitrary splittings and real mixed double Hurwitz numbers. Under certain conditions, we find lower bounds for these real analogues, and obtain logarithmic asymptotics for real monotone double Hurwitz numbers relative to arbitrary splittings and real mixed double Hurwitz numbers. In particular, under given conditions real mixed double Hurwitz numbers are logarithmically equivalent to complex double Hurwitz numbers. We construct a family of real tropical covers and use them to show that real monotone double Hurwitz numbers relative to simple splittings are logarithmically equivalent to monotone double Hurwitz numbers with specific conditions. This is consistent with the logarithmic equivalence of real double Hurwitz numbers and complex double Hurwitz numbers.

Exploring the Potential of Nano-Priming and Magneto-Priming in Enhancing Drought Tolerance Potential of Wheat Seeds

The current study was aimed to explore the effects of two priming treatments, Nano-Priming (NP) and Magneto-Priming (MP) on improving the drought tolerance potential in wheat. Study revealed increase in germination efficiency in both the priming treatments compared to control Unprimed (UP) seeds. NP seeds exhibited a significant improvement in parameters such as germination percentage, seedling length, and seedling vigor when compared to both MP and UP seeds. The impact of Drought Stress (DS) on photosynthetic efficiency measured using Chl a fluorescence parameters, revealed a drastic reduction in the number of active Reaction Centers (RC) per chlorophyll molecule, performance of water splitting complex at donor side of PSII (Fv/Fo) and plant Performance Index (PI) in UP and MP plants wheat plants. However, NP+DS plants seemed to have improved the efficiency of primary photochemistry of PSII by showing significantly lesser reduction in these parameters under DS, ultimately resulting in better growth. Furthermore, the investigation of the oxidative status of plants revealed a reduction in the activity of antioxidant enzymes in NP + DS plants, potentially linked to reduced levels of reactive oxygen species production when compared to UP + DS plants. These findings suggest NP as an effective yet simple way for augmenting the drought tolerance potential in wheat.

Low-temperature oxidation characteristics and reaction pathways of crude oil within tight shale during air injection

The investigation of low-temperature oxidation (LTO) of crude oil within tight shale holds significant importance due to its implications for subsequent oxidation reactions and enhanced oil recovery in the process of air injection. In this study, the tight shale sample underwent oxidation at various LTO temperatures, followed by an analysis of the resulting gas composition. Furthermore, the oxidized oil was separated from the tight shale and subjected to characterization using electron paramagnetic resonance, nuclear magnetic resonance, and negative ion electrospray Fourier transform-ion cyclotron resonance mass spectrometry techniques. The primary focus was on examining the distinct LTO reaction pathways observable across different temperature ranges. The findings demonstrated a correlation between LTO temperature and the concentration of free radicals, which predominantly resided on aromatic hydrocarbons, alkanes, and oxygen atoms. Additionally, the proton count of polycyclic aromatic hydrocarbons exhibited a continuous increase from 83 to 350 °C, suggesting intensified aromatization and condensation reactions involving aliphatic and aromatic compounds. With rising LTO temperature, the molecular structure of O2 compounds underwent significant transformations, characterized by increased condensation degree and a decrease in low carbon number molecular structures, while higher equivalent double bonds and carbon number molecular structures became more prevalent. The influence of cycle path 1 diminished at temperatures ranging from 83 to 150 °C and 250 to 350 °C, whereas the significance of cycle paths 2 and 3 increased, resulting in an overall escalation of the oxidation rate with temperature elevation. It was observed that the shale oil LTO process exhibited a negative temperature coefficient within the temperature range of 150-250 °C, emphasizing the criticality of overcoming the energy barrier in this region to achieve stable combustion. This comprehensive investigation provides valuable insights into the mechanisms underlying LTO in crude oil confined within tight shale.

Hyperbolic Actions and 2nd Bounded Cohomology of Subgroups of 𝖮𝗎𝗍(𝖥_{𝗇})

In this two part work we prove that for every finitely generated subgroup Γ &gt; O u t ( F n ) \Gamma &gt;{\mathsf {Out}}(F_n) , either Γ \Gamma is virtually abelian or H b 2 ( Γ ; R ) H^2_b(\Gamma ;{\mathbb {R}}) contains a vector space embedding of ℓ 1 \ell ^1 . The method uses actions on hyperbolic spaces. In Part I we focus on the case of infinite lamination subgroups Γ \Gamma —those for which the set of all attracting laminations of all elements of Γ \Gamma is an infinite set—using actions on free splitting complexes of free groups. In Part II we focus on finite lamination subgroups Γ \Gamma and on the construction of useful new hyperbolic actions of those subgroups.

Qualitative characterization of oxygen-containing compounds in fuel extracts by using (-) electrospray ionization coupled to a linear quadrupole ion trap/orbitrap mass spectrometer

Qualitative characterization of oxygen-containing compounds (OCCs) in fuels is imperative, as these compounds detrimentally influence fuel stability. Hence, development of analytical methods that enable thorough qualitative information will likely enhance correlations between composition and fuel failures. In this work, (-) electrospray ionization (ESI)coupled to a linear quadrupole ion trap/orbitrap mass spectrometer provided detailed qualitative analysis of OCCs in jet fuels, marine gas oil (MGO)and diesel. The high resolving power and mass accuracy of the orbitrap and soft ionization of ESI advanced the current OCC qualitative knowledge of fuels as the number of OCCs classes identified exceeded previous works. Up to nine, twenty and nine different homologue ion series (i.e.,ions with the same empirical formula (e.g.,CnH2n-7O) but differ by 14 Da (m/z 149, 163, 177, etc.)) were detected in the jet fuels, diesel and MGO, respectively. Additional detailed qualitative information included the average ring and double equivalent values, carbon numbers and molecular weights for the detected OCCs in each fuel. With limited fragmentation of ions, Kendrick Mass Defectplots were made that enabled straightforward comparison of the OCC compositions offuels. Clear qualitative differences were noted among the different types of fuels (i.e.,jet fuels compared to diesel) and when the threejet fuels were compared to each other. As the method demonstrated proficiency at providing detailed compositional information, it may be employed for future storage and thermal stress testing of fuels to monitor and evaluate compositional changes. Overall, the method demonstrated qualitative proficiency and may be used to establish important links between composition and fuel stability; this is a critical prerequisite for improving fuel quality.

Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers

We derive an explicit formula for the connected $(n,m)$-point functions associated to an arbitrary diagonal tau-function $\tau_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$ of the 2d Toda lattice hierarchy using fermionic computations and the boson-fermion correspondence. Then for fixed $\boldsymbol{t}^-$, we compute the KP-affine coordinates of $\tau_f(\boldsymbol{t}^+,\boldsymbol{t}^-)$. As applications, we present a unified approach to compute various types of connected double Hurwitz numbers, including the ordinary double Hurwitz numbers, the double Hurwitz numbers with completed $r$-cycles, and the mixed double Hurwitz numbers. We also apply this method to the computation of the stationary Gromov-Witten invariants of $\mathbb P^1$ relative to two points.

Asynchronous generator replacement scheme with internal capacitive reactive power compensation

The relevance of using compensated induction machines in the generator mode of autonomous power supply systems is determined by their ability to provide a stable and reliable power supply even in the absence of an external grid. The research aims to develop a procedure for determining the characteristics of an equivalent circuit of compensated induction generators that considers the mutual influence between the main and additional phase windings of the armature. The theory of an idealised induction machine with the representation of electromechanical energy conversion processes and basic physical parameters in the form of equations of electrical equilibrium and drive motion was used to obtain the calculated characteristics of the generator’s operating modes of this class. The generalised system of differential equations made it possible to calculate dynamic and static processes for symmetrical and asymmetrical modes at given machine parameters under different methods of excitation and voltage stabilisation under variable load. For the practical implementation of modelling the parameters of an induction generator, the equations of electrical equilibrium of the stator and rotor circuits for the symmetrical steady-state mode are used, which is a special case of the generalised mathematical model of the machine for both transient and steady-state processes with constant parameters of the substitution scheme. Consideration of the structural and functional features of compensated induction generators was made possible by using a mathematical model with the armature winding divided into two coaxial or spatially offset half-windings. In this case, the number of calculation equations doubles. The use of an autotransformer scheme for switching on the stator phase half-windings to capacitors required the introduction of an additional differential equation for the electrical equilibrium of the stator phases. This made it possible to substantiate the values of active and inductive resistances used in the replacement circuit of an induction generator with internal capacitive reactive power compensation. The mutual inductive coupling of the main and additional half-windings of the generator stator phase windings due to both the operating magnetic flux and the magnetic fluxes of dissipation was considered. The practical significance of the obtained results is to increase the efficiency and stability of the power supply, which helps to reduce losses and improve the operation of electric power systems

Lipidomics analysis of impaired glucose tolerance and type 2 diabetes mellitus in overweight or obese elderly adults.

Aging, obesity, and type 2 diabetes mellitus (T2DM) form a metabolic disease continuum that has a continuously increasing prevalence. Lipidomics explains the complex interactions between lipid metabolism and metabolic diseases. We aimed to systematically investigate the plasma lipidome changes induced by newly diagnosed impaired glucose tolerance (IGT) and T2DM in overweight/obese elderly individuals and to identify potential biomarkers to differentiate between the IGT, T2DM, and control groups. Plasma samples from 148 overweight/obese elderly individuals, including 52 patients with IGT, 47 patients with T2DM, and 49 euglycemic controls, were analyzed using a high-coverage nontargeted absolute quantitative lipidomics approach. We quantified 1840 lipids from thirty-eight classes and seven lipid categories. Among overweight/obese elderly individuals, the lipidomic profiles of IGT and T2DM patients were significantly different from those of controls, while they were similar in the IGT and T2DM groups. The concentrations of diglycerides, triglycerides, phosphatidylcholines, and ceramides were obviously altered in the IGT and T2DM groups. Particularly, IGT and T2DM induced the accumulation of triglycerides with longer carbon atom numbers (C44-50) and saturated or lower double bond numbers (n (C=C) = 0-2). Furthermore, a total of 17 potential lipidic biomarkers were identified to successfully differentiate between the IGT, T2DM, and control groups. In overweight/obese elderly patients, IGT and T2DM induced apparent lipidome-wide changes. This study's results may contribute to explaining the complex dysfunctional lipid metabolism in aging, obesity, and diabetes.

Global Analysis of 2-Hydroxy Fatty Acids by Gas Chromatography-Tandem Mass Spectrometry Reveals Species-Specific Enrichment in Echinoderms.

Abnormal levels of 2-hydroxy fatty acids (2-OH FAs) are characterized in multiple diseases, and their quantification in foodstuffs is critical to identify the sources of supplementation for potential treatment. However, due to the structural complexity and limited available standards, the comprehensive profiling of 2-OH FAs remains an ongoing challenge. Herein, an innovative approach based on gas chromatography-tandem mass spectrometry (GC-MS/MS) was developed to determine the full profile of these FA metabolites. MS and MS/MS spectra of the trimethylsilyl (TMS) derivatives of 2-OH fatty acid methyl esters (FAMEs) were collected for peak annotation by their signature fragmentation patterns. The structures were further confirmed by validated structure-dependent retention time (RT) prediction models, taking advantage of the correlation between the RT, carbon chain length, and double bond number from commercial standards and pseudostandards identified in the whole-brain samples from mice. An in-house database containing 50 saturated and monounsaturated 2-OH FAs was established, which is expandible when additional molecular species with different chain lengths and backbone structures are identified in the future. A quantitation method was then developed by scheduled multiple reaction monitoring (MRM) and applied to investigate the profiling of 2-OH FAs in echinoderms. Our results revealed that the levels of total 2-OH FAs in sea cucumber Apostichopus japonicas (8.40 ± 0.28 mg/g dry weight) and starfish Asterias amurensis (7.51 ± 0.18 mg/g dry weight) are much higher than that in sea urchin Mesocentrotus nudus (531 ± 108 μg/g dry weight). Moreover, 2-OH C24:1 is the predominant molecular species accounting for 67.9% of the total 2-OH FA in sea cucumber, while 2-OH C16:0 is the major molecular species in starfish. In conclusion, the current innovative GC-MS approach has successfully characterized distinct molecular species of 2-OH FAs that are highly present in sea cucumbers and starfish. Thus, these findings suggest the possibility of developing future feeding strategies for preventing and treating diseases associated with 2-OH FA deficiency.