Homogeneous Components Research Articles

Identities and cocharacters of the algebra of 3 × 3 matrices with non-trivial grading and transpose graded involution

Let F be a field of characteristic zero and M2,1(F) the algebra of 3×3 matrices over F endowed with non-trivial Z2-grading. The transpose involution t on M2,1(F) preserves the homogeneous components of the grading and so, we consider (M2,1(F),t) as a superalgebra with graded involution. We study the (Z2,⁎)-identities of this algebra and make explicit the decomposition of the space of multilinear (Z2,⁎)-identities into the sum of irreducibles under the action of the group (Z2×Z2)≀Sn in order to determine all the irreducible characters appearing with non-zero multiplicity in the decomposition of the ⁎-graded cocharacter of (M2,1(F),t). Along the way, using the representation theory of the general linear group, we determine all the (Z2,⁎)-identities of (M2,1(F),t) up to degree 3.

Effect of deposit thickness on microstructure and mechanical properties at ambient and elevated temperatures for Inconel 718 superalloy fabricated by directed energy deposition

The effect of deposit thickness on the microstructure and the mechanical properties of Inconel 718 (IN718) fabricated by directed energy deposition was systematically investigated in both as-deposited (AD) and homogenization + solution + aging (HSA) treated conditions. Results indicate that deposit thickness for thin parts has a more significant impact on the microstructure and subsequent room (RT) and elevated temperature (650 °C) tensile properties compared to thick parts. Applying HSA treatment can effectively homogenize the microstructure of thick builds with a microstructure transition from columnar-dendritic grain structure presented in the AD condition to recrystallized equiaxted grain structure, which results in almost similar yield strength, ultimate tensile strength and ductility of ~ 970 MPa, ~ 1237 MPa, ~ 20% at RT and ~ 816 MPa, ~ 954 MPa, ~ 12% at 650 °C, respectively. In contrast, thin parts maintaining columnar grain features during HSA treatment yield a higher yield strength of 1112 MPa (increased by 15%) at RT and 936 MPa (increased by 15%) at 650 °C, but much lower ductility of 9% (decreased by 54%) at RT and 6% MPa (decreased by 51%) at 650 °C. The remaining large amount of residual stress primarily contribute to the enhancement of yield strength, as well as large amount of δ phase responsible for the much worse ductility for thin parts after HSA treatment. In addition, the underlying thermal history evolution in various deposit thickness is elucidated by the thermal simulations with the use of Finite Element Method (FEM) method within 3DExperience software. The results present in the current study show the capability of the directed energy deposition process to manufacture homogeneous components with varying thickness for high temperature application after a proper heat treatment, with regard to their initial as-deposited materials.

Implementation of reengineering technology to reduce the terms of the technical preparation of manufacturing of aviation technology assemblies

The object of this study is the technical preparation of manufacturing (TPM) of aviation technology (AT) using reengineering technology. The task to reduce the terms of TPM AT was tackled while solving direct and inverse problems of shape formation involving reengineering. The study is based on the equation for calculating the labor intensity of creating an assembly unit (AU) as a mathematical model for the formation and accumulation of components of the total labor intensity at all stages. The following results are reported: a scheme has been proposed for linking homogeneous components of an article obtained using the loft-template method (LTM) with digital mock-up (DMU) when applying the reengineering method. The scheme summarizes and structures the reengineering technology to solve direct and inverse shape-formation problems and could be used to solve the tasks of prototyping, manufacturing, and refurbishment of tooling, as well as article control at all stages of production. An example of the helicopter stabilizer shows that when solving the direct shape-formation problem, the labor intensity is from 294.94 to 315.06 man-hours, and when solving the inverse problem ‒ from 194.78 to 213.22 man-hours. A comparative analysis of the labor intensity of TPM revealed a difference of 1.5 times in favor of the labor intensity of solving the inverse problem. Comparing the labor intensity of creating DMU for the stabilizer of a helicopter has made it possible to establish that the labor intensity of solving the inverse problem is 3.7 times less than the labor intensity of solving a direct problem. Recommendations for reducing the terms of TPM AT with the use of reengineering are given. The results could be used to assess the labor intensity and timing of TPM AT and mechanical engineering objects in general when using reengineering technology

Sulphite addition during steam pretreatment enhanced both enzyme-mediated cellulose hydrolysis and ethanol production

Sulphite addition during steam pretreatment of softwoods under acidic, neutral and alkaline conditions was assessed to try to minimize lignin condensation. Although pretreatment under neutral/alkaline conditions resulted in effective lignin sulphonation, non-uniform size reduction was observed. In contrast, acidic sulphite steam treatment at 210 °C for 10 min resulted in homogenous particle size reduction and water-insoluble component that was 62% carbohydrate and 33% lignin. This carbohydrate-rich substrate was readily hydrolyzed and fermented which indicated the lack of fermentation inhibitors in the steam-pretreated whole slurry. The use of high solid loading (25% w/v) resulted in a hydrolysis yield of 58% at an enzyme loading of 40 mg protein/g glucan and efficient fermentation (46.6 g/L of ethanol). This indicated that the addition of acidic sulphite at the steam pretreatment of softwoods improved both the enzymatic hydrolysis and fermentation of steam-pretreated whole slurries.Graphical

ЛІНГВАЛЬНА АРГУМЕНТАЦІЯ В СУЧАСНОМУ РЕКЛАМНОМУ ДИСКУРСІ США

The article is devoted to the analysis of the speech implementation of the strategy of argumentative impact on the addressee in the English advertising discourse, which is a combination of peculiarly organized texts, which according to the type of speech impact are conditionally divided into informative, argumentative, suggestive and manipulative. The strategy of argumentative impact is to convince the addressee of the feasibility of choosing a particular product (service), based on the use of rational and psychological arguments and is implemented through appropriate tactics. Tactics of creating a logical chain involves the use of logical arguments aimed at highlighting the important properties of the product (service). Tactics of detailing is a thorough description of the positive characteristics of the product (service) with the involvement of factual information. Tactics of motivation is to highlight an important motive, because it is the motive is an internal psychological state that motivates the individual to take action. Typical linguistic and stylistic means of implementing tactics of argumentative strategy are usually the use of neologisms to denote favorable arguments to the addressee, numerals with specific clarifications, syntactic constructions with subordinate causes, goals, modes of action, expressing logical arguments, sentences with homogeneous components.

Pd Complex of Ferrocenylphosphine Supported on Magnetic Nanoparticles: A Highly Reusable Catalyst for Transfer Hydrogenation and Coupling Reactions

In this study, diphenylphosphino-ferrocenylethylamine conjugated with dopamine and complexed with Pd metal and anchored on magnetic nanoparticles is used as a reusable catalyst for the transformation of a series of organic functional groups. The prepared catalyst composed of a homogeneous component (ligand) attached to the heterogeneous part (Fe3O4) was characterized using FTIR, XRD, SEM, TEM, and XPS. A wide variety of catalytic reactions, such as transfer hydrogenation (TH) and coupling reaction, was investigated. Nitrophenol, one of the pollutants in groundwater, is straightforwardly hydrogenated to produce the corresponding aromatic amine with >99% selectivity using tetrahydroxydiboron as the hydrogen source in water. Styrene is selectively hydrogenated to produce ethylbenzene also in water. Mizoriki-Heck and Suzuki-Miyuara cross-coupling reactions produce excellent results in higher olefin synthesis and biphenyl formation under basic conditions. The catalyst displays high structural stability and can be reused multiple times without supplementing the catalyst. A facile and balancing combination between an organic coordination complex capable of catalyzing reactions with an ultrasmall magnetic solid support allows the convenient separation of the catalyst from the reaction mixture.

K-theoretic Catalan functions

We prove that the K-k-Schur functions are part of a family of inhomogenous symmetric functions whose top homogeneous components are Catalan functions, the Euler characteristics of certain vector bundles on the flag variety. Lam-Schilling-Shimozono identified the K-k-Schur functions as Schubert representatives for K-homology of the affine Grassmannian for SLk+1. Our perspective reveals that the K-k-Schur functions satisfy a shift invariance property, and we deduce positivity of their branching coefficients from a positivity result of Baldwin and Kumar. We further show that a slight adjustment of our formulation for K-k-Schur functions produces a second shift-invariant basis which conjecturally has both positive branching and a rectangle factorization property. Building on work of Ikeda-Iwao-Maeno, we conjecture that this second basis gives the images of the Lenart-Maeno quantum Grothendieck polynomials under a K-theoretic analog of the Peterson isomorphism.

Solution for optimal control of general nonlinear systems using generating functions

AbstractIn this paper, we present an analytical local solution for optimal control problems applicable to a wide class of general nonlinear systems. We first introduce the optimal control problem for a general nonlinear system and formulate the associated Hamilton–Jacobi–Bellman equation. Starting from the necessary conditions for optimality represented by the Hamiltonian system of the optimal control problem, we solve the Hamilton–Jacobi equation for the associated generating functions. The generating functions are obtained in the form of series expansions by using canonical transformation theory and the semi‐tensor product of matrices. The coefficients of the generating functions satisfy simply the algebraic Riccati equation and linear algebraic equations for the second‐degree homogeneous component and higher degree components, respectively, from which an algorithm and data structure can be derived. This enables us to obtain analytical optimal feedback controllers and the corresponding Lyapunov function. Through theoretical analysis, it is established that the proposed methodology guarantees stability of the closed‐loop system. This approach is not affected by the complexity of the performance index and state equations, and most importantly, it does not require any initial admissible control law. A simulation example is presented to illustrate the effectiveness and applicability of the proposed approach.

On graded classical 2-absorbing second submodules of graded modules over graded commutative rings

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded classical and graded strongly classical 2-absorbing second submodules of graded modules over a graded commutative rings. A number of results concerning these classes of graded submodules and their homogeneous components are given.

Nested spheroidal figures of equilibrium I. Approximate solutions for rigid rotations

ABSTRACT We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient pressure), approximations can be obtained for configurations involving a small confocal parameter. The problem then admits two families of solutions, depending on the pressure along the common interface (constant or quadratic with the cylindrical radius). We give in both cases the pressure and the rotation rates as a function of the fractional radius, ellipticities, and mass–density jump. Various degrees of flattening are allowed but there are severe limitations for global rotation, as already known from classical theory (e.g. impossibility of confocal and coelliptical solutions, gradient of ellipticity outward). States of relative rotation are much less constrained, but these require a mass–density jump. This analytical approach compares successfully with the numerical solutions obtained from the self-consistent-field method. Practical formula are derived in the limit of small ellipticities appropriate for slowly rotating star/planet interiors.

Extraction Optimization, Structural Characterization, and Anti-Hepatoma Activity of Acidic Polysaccharides From Scutellaria barbata D. Don.

The Chinese medicinal herb Scutellaria barbata D. Don has antitumour effects and is used to treat liver cancer in the clinic. S. barbata polysaccharide (SBP), one of the main active components extracted from S. barbata D. Don, exhibits antitumour activity. However, there is still a lack of research on the extraction optimization, structural characterization, and anti-hepatoma activity of acidic polysaccharides from S. barbata D. Don. In this study, the optimal extraction conditions for SBP were determined by response surface methodology (RSM): the material-liquid ratio was 1:25, the extraction time was 2 h, and the extraction temperature was 90°C. Under these conditions, the average extraction efficiency was 3.85 ± 0.13%. Two water-soluble polysaccharides were isolated from S. barbata D. Don, namely, SBP-1A and SBP-2A, these homogeneous acidic polysaccharide components with average molecular weights of 1.15 × 105 Da and 1.4 × 105 Da, respectively, were obtained at high purity. The results showed that the monosaccharide constituents of the two components were fucose, galactosamine hydrochloride, rhamnose, arabinose, glucosamine hydrochloride, galactose, glucose, xylose, and mannose; the molar ratio of these constituents in SBP-1A was 0.6:0.3:0.6:30.6:3.3:38.4:16.1:8:1.4, and that in SBP-2A was 0.6:0.5:0.8:36.3:4.4:42.7:9.2:3.6:0.7. In addition, SBP-1A and SBP-2A contained uronic acid and β-glucan, and the residue on the polysaccharide was mainly pyranose. The in vitro results showed that the anti-hepatoma activity of SBP-2A was better than that of SBP-1A and SBP. In addition, SBP-2A significantly enhanced HepG2 cell death, as cell viability was decreased, and SBP-2A induced HepG2 cell apoptosis and blocked the G1 phase. This phenomenon was coupled with the upregulated expression of P53 and Bax/Bcl-2 ratio, as well as the downregulated expression of the cell cycle-regulating protein cyclinD1, CDK4, and Bcl-2 in this study. Further analysis showed that 50 mg/kg SBP-2A inhibited the tumour growth in H22 tumour-bearing mice, with an average inhibition rate of 40.33%. Taken together, SBP-2A, isolated and purified from S. barbata showed good antitumour activity in vivo and in vitro, and SBP-2A may be a candidate drug for further evaluation in cancer prevention. This study provides insight for further research on the molecular mechanism of the anti-hepatoma activity of S. barbata polysaccharide.

Mixed scale dense convolutional networks for x-ray phase contrast imaging

X-ray in-line phase contrast imaging relies on the measurement of Fresnel diffraction intensity patterns due to the phase shift and the attenuation induced by the object. The recovery of phase and attenuation from one or several diffraction patterns is a nonlinear ill-posed inverse problem. In this work, we propose supervised learning approaches using mixed scale dense (MS-D) convolutional neural networks to simultaneously retrieve the phase and the attenuation from x-ray phase contrast images. This network architecture uses dilated convolutions to capture features at different image scales and densely connects all feature maps. The long range information in images becomes quickly available, and greater receptive field size can be obtained without losing resolution. This network architecture seems to account for the effect of the Fresnel operator very efficiently. We train the networks using simulated data of objects consisting of either homogeneous components, characterized by a fixed ratio of the induced refractive phase shifts and attenuation, or heterogeneous components, consisting of various materials. We also train the networks in the image domain by applying a simple initial reconstruction using the adjoint of the Fréchet derivative. We compare the results obtained with the MS-D network to reconstructions using U-Net, another popular network architecture, as well as to reconstructions using the contrast transfer function method, a direct phase and attenuation retrieval method based on linearization of the direct problem. The networks are evaluated using simulated noisy data as well as images acquired at NanoMAX (MAX IV, Lund, Sweden). In all cases, large improvements of the reconstruction errors are obtained on simulated data compared to the linearized method. Moreover, on experimental data, the networks improve the reconstruction quantitatively, improving the low-frequency behavior and the resolution.

Load aliasing—A new additional test concept for effective control of nonhomogeneous high‐frequency behavior in linear multistep methods

AbstractThis article introduces a new additional test concept and numerical property of implicit time integration methods termed as “aliasing” of the external load which must be considered during the algorithm design process. Where most numerical properties of such algorithms discussed in the literature pertain to the homogeneous components, aliasing reflects the tendency of the nonhomogeneous components to introduce errors into the solution in the asymptotic high‐frequency limit. An analytical technique is proposed to detect and quantify aliasing, defined in terms of the resulting representative solution. A theorem establishes whether a representative solution with aliasing can be bounded up to a constant by the external force values and thus treated as acceptable if the bound is sufficiently small. For the U0 family of algorithms within the GSSSS‐II framework containing several traditional and closely related methods, this is not an issue. However, the numerically dissipative GSSSS‐II V0 family of methods is shown to exhibit bounded aliasing with a constant roughly equal to 2, while the “structure‐dependent” Chang Family Method is shown to exhibit unbounded aliasing, which is not acceptable for practical dynamic computations. Numerical verifications are performed with single‐degree and multi‐degree of freedom problems with a series of selected algorithms which exhibit either no aliasing, tightly bounded aliasing, unbounded aliasing, or large bounded aliasing, and practical recommendations are given for acceptable aliasing of the load with special emphasis on MDOF problems such as those arising from finite element discretizations.

Manipulating thermal fields with inhomogeneous heat spreaders

We design a class of spatially inhomogeneous heat spreaders in the context of steady-state thermal conduction leading to spatially uniform thermal fields across a large convective surface. Each spreader has a funnel-shaped design, either in the form of a trapezoidal prism or truncated cone, and is forced by a thermal source at its base. We employ transformation-based techniques, commonly used to study metamaterials, to determine the required thermal conductivity for the spreaders. The obtained materials, although strongly anisotropic and inhomogeneous, are accurately approximated by assembling isotropic, homogeneous layers, rendering them realisable. An alternative approach is then considered for the conical and trapezoidal spreaders by dividing them into two or three isotropic, homogeneous components respectively. We refer to these simple configurations as neutral layers. All designs are validated numerically both with and without the effects of thermal contact resistance between layers. Such novel designs pave the way for future materials that can manipulate and control the flow of heat, helping to solve traditional heat transfer problems such as controlling the temperature of an object and energy harvesting.

Quantum queer supergroups via υ-differential operators

By using certain quantum differential operators, we construct a super representation for the quantum queer supergroup Uυ(qn). The underlying space of this representation is a deformed polynomial superalgebra in 2n2 variables whose homogeneous components can be used as the underlying spaces of queer q-Schur superalgebras. We then extend the representation to its formal power series algebra which contains a (super) submodule isomorphic to the regular representation of Uυ(qn). A monomial basis M for Uυ(qn) plays a key role in proving the isomorphism. In this way, we may present the quantum queer supergroup Uυ(qn) by another new basis L together with some explicit multiplication formulas by the generators. As an application, similar presentations are obtained for queer q-Schur superalgebras via the above mentioned homogeneous components.The existence of the bases M and L and the new presentation show that the seminal construction of quantum gln established by Beilinson–Lusztig–MacPherson thirty years ago extends to this “queer” quantum supergroup via a completely different approach.

Structural properties, antioxidant and hypoglycemic activities of polysaccharides purified from pepper leaves by high-speed counter-current chromatography

In the present study, polysaccharides with antioxidant and hypoglycemic activities were isolated from the crude extract of pepper leaves by high-speed countercurrent chromatography in one step for the first time. An aqueous polymer two-phase system comprising PEG1000-K2HPO4-KH2PO4-H2O (0.8:1.25:1.25:6.5, w/w) was used for separation. During each separation, 2.0 g of the crude sample yielded two homogeneous components of polysaccharides PLP1 (226 mg) and PLP2 (273 mg). The molecular weights of PLP1 and PLP2 were 123 kDa and 243 kDa, respectively. PLP1 primarily consisted of mannose and glucose at a molar ratio of 1:2.4, whereas PLP2 was mainly composed of galactose, glucose, and rhamnose at a molar ratio of 2.6:1:2.2 with 10.3% (w/w) sulphates. Biological activity showed that sulfated PLP2 exhibited stronger antioxidant activity in vitro and hypoglycemic activity in diabetic mice than PLP1. The results demonstrated that sulfated PLP2 possessed potential as natural hypoglycemic agents or antioxidants in food or pharmaceuticals.

Parametric pseudodifferential operators with point-singularity in the covariable

Starting out from a new description of a class of parameter-dependent pseudodifferential operators with finite regularity number due to G. Grubb, we introduce a calculus of parameter-dependent, poly-homogeneous symbols whose homogeneous components have a particular type of point-singularity in the covariable-parameter space. Such symbols admit intrinsically a second kind of expansion which is closely related to the expansion in the Grubb–Seeley calculus and permits to recover the resolvent-trace expansion for elliptic pseudodifferential operators originally proved by Grubb–Seeley. Another application is the invertibility of parameter-dependent operators of Toeplitz type, i.e., operators acting in subspaces determined by zero-order pseudodifferential idempotents.

Reliability analysis of load-sharing systems with spatial dependence and proximity effects

In the operating process of multi-component systems, components may interact with each other in a way that the load of a failed component is taken up by its nearby components at varying proportions. As a result, the failure rates of the proximate components are accelerated while distant components are not affected. This paper develops a novel spatial model for estimating the reliability of a load-sharing system considering spatial dependence and proximity effects. The spatial model is applicable to systems with heterogeneous or homogeneous components and is suitable for systems with or without distance information. To investigate the importance and significance of the spatial effect, we compare our spatial model with an equal load-sharing through numerical examples. Our results demonstrate that our model is more accurate than standard load sharing models in evaluating system reliability when spatial effects exist.

A sandwich in thin lie algebras

AbstractA thin Lie algebra is a Lie algebra $L$, graded over the positive integers, with its first homogeneous component $L_1$ of dimension two and generating $L$, and such that each non-zero ideal of $L$ lies between consecutive terms of its lower central series. All homogeneous components of a thin Lie algebra have dimension one or two, and the two-dimensional components are called diamonds. Suppose the second diamond of $L$ (that is, the next diamond past $L_1$) occurs in degree $k$. We prove that if $k>5$, then $[Lyy]=0$ for some non-zero element $y$ of $L_1$. In characteristic different from two this means $y$ is a sandwich element of $L$. We discuss the relevance of this fact in connection with an important theorem of Premet on sandwich elements in modular Lie algebras.

Genomic Insights Into the Population History and Biological Adaptation of Southwestern Chinese Hmong-Mien People.

Hmong–Mien (HM) -speaking populations, widely distributed in South China, the north of Thailand, Laos, and Vietnam, have experienced different settlement environments, dietary habits, and pathogenic exposure. However, their specific biological adaptation remained largely uncharacterized, which is important in the population evolutionary genetics and Trans-Omics for regional Precision Medicine. Besides, the origin and genetic diversity of HM people and their phylogenetic relationship with surrounding modern and ancient populations are also unknown. Here, we reported genome-wide SNPs in 52 representative Miao people and combined them with 144 HM people from 13 geographically representative populations to characterize the full genetic admixture and adaptive landscape of HM speakers. We found that obvious genetic substructures existed in geographically different HM populations; one localized in the HM clines, and others possessed affinity with Han Chinese. We also identified one new ancestral lineage specifically existed in HM people, which spatially distributed from Sichuan and Guizhou in the north to Thailand in the south. The sharing patterns of the newly identified homogenous ancestry component combined the estimated admixture times via the decay of linkage disequilibrium and haplotype sharing in GLOBETROTTER suggested that the modern HM-speaking populations originated from Southwest China and migrated southward in the historic period, which is consistent with the reconstructed phenomena of linguistic and archeological documents. Additionally, we identified specific adaptive signatures associated with several important human nervous system biological functions. Our pilot work emphasized the importance of anthropologically informed sampling and deeply genetic structure reconstruction via whole-genome sequencing in the next step in the deep Chinese Population Genomic Diversity Project (CPGDP), especially in the regions with rich ethnolinguistic diversity.