On steady rotations of a rigid body bearing a single-axis powered gyroscope whose precession axis is parallel to a principal plane of inertia

The set of steady motions of the system named in the title is represented parametrically via the gyro gimbal rotation angle for an arbitrary position of the gimbal axis.We study the set of steady motions for a system in which the gyro gimbal axis is parallel to a principal plane of inertia as well as for a system with a dynamic symmetry. We determine all motions satisfying sufficient stability conditions. In the presence of dissipation in the gimbal axis, we use the Barbashin-Krasovskii theorem to identify each steady motion as either conditionally asymptotically stable or unstable.     

Functionalization of Pasteurized Milk Using Rosemary,Thyme, and Ammoides Aqueous Extracts for Better Microbial Quality and an Improved Antioxidant Activity

This study aimed to evaluate the effects of thyme (Thymus vulgaris L.), rosemary (Rosmarinus officinalis L.), and ammoides (Ammoidespusilla L.) aqueous extracts supplementation on the quality of heat-treated (55, 65, and 75 °C) raw milk (sample lots: A, B, and C) and cold-stored pasteurized milk (lot D). The three herbs have shown rich polyphenol contents (32.65–104.23 mgGAE/g), relevant antioxidant capacity, and high caffeic and rosmarinic acids and catechin contents. A significant reduction in psychrotrophic and total viable bacteria counts (PC and TVC) was attained following milk extract supplementation in both experiments. Monitoring PC and TVC counts in sample lots (A, B, and C) has revealed a significant improvement in extracts’ effectiveness in reducing the TVC count with the increment of temperature. The highest reductions of PC and TVC counts were achieved, respectively, in samples treated with thyme and rosemary in (lots: A, B, and C) and in samples treated with ammoides and thyme in (lot D). Thyme extract showed the highest milk serum DPPH scavenging activity (74.84% at 0.1 mg/mL) and induced a significant Listeria monocytogenes growth inhibition (>1 Log cycle). The sensory evaluation of supplemented milk has shown good consumer acceptability of ammoides-supplemented milk, quite similar to the control sample.     

Formation of an Ni7(μ3-OH)6(η-OOCBu t )6(μ3-OOCBu t )2(Hdmpz)6 cluster during the thermolysis of binuclear complex Ni2(μ-OOCBu t )4(Hdmpz)2 (Hdmpz = 3,5-dimethylpyrazole)

Cluster Ni₇(μ₃-OH)₆(OOCBu ^t )₈(Hdmpz)₆ was found to form as a result of the thermal destruction of complex Ni₂(μ-OOCBu ^t )₄(Hdmpz)₂ at 190°C. The cluster was characterized using X-ray crystallography.     

Structural,elastic, thermodynamic and electronic properties of LuX (X = N,Bi and Sb) compounds: first principles calculations

ABSTRACT

The structural, electronic, elastic and thermodynamic properties of LuX (X = N, Bi and Sb) based on rare earth into phases, Rocksalt (B1) and CsCl (B2) have been investigated using full-potential linearized muffin-tin orbital method (FP-LMTO) within density functional theory. Local density approximation (LDA) for exchange-correlation potential and local spin density approximation (LSDA) are employed. The structural parameters as lattice parameters a₀, bulk modulus B, its pressure derivate B’ and cut-off energy (E_c) within LDA and LSDA are presented. The elastic constants were derived from the stress–strain relation at 0 K. The thermodynamic properties for LuX using the quasi-harmonic Debye model are studied. The temperature and pressure variation of volume, bulk modulus, thermal expansion coefficient, heat capacities, Debye temperature and Gibbs free energy at different pressures (0–50 GPa) and temperatures (0–1600 K) are predicted. The calculated results are in accordance with other data.     

LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL SYSTEMS

Using the averaging theory of first and second order we study the maximum number of limit cycles of generalized Linard differential systems{x = y + εh_l~1(x) + ε~2h_l~2(x),y=-x- ε(f_n~1(x)y~(2p+1) + g_m~1(x)) + ∈~2(f_n~2(x)y~(2p+1) + g_m~2(x)),which bifurcate from the periodic orbits of the linear center x = y,y=-x,where ε is a small parameter.The polynomials h_l~1 and h_l~2 have degree l;f_n~1and f_n~2 have degree n;and g_m~1,g_m~2 have degree m.p ∈ N and[·]denotes the integer part function.     

Bioassay-guided isolation and POM analyses of a new immunomodulatory polyphenolic constituent from Callistemon viridiflorus

Chromatographic separation of 80% EtOH extract of Callistemon viridiflorus leaves led to the isolation of six known constituents (1–6) along with a new polyphenolic compound 7 identified as apigenin 4′-O-β-d-glucopyranosyl-(1″′ → 4″)-O-β-d-glucopyranoside. The ethanolic extract of C. viridiflorus leaves and isolated compounds were evaluated for in vitro immunomodulatory activity by means of RAW 264.7 macrophages proliferation (MTT) assay. Ethanolic extract of leaves and compounds 1, 3, 4, 6 and 7 caused a significant increase in macrophage proliferation; these findings may suggest that this medicinal plant could be utilised as an excellent source of compounds for immunomodulatory activity.     

Fixed point theorems for the sum of ( ws)-compact and asymptotically $${\Phi}$$-nonexpansive mappings

In this paper, we introduce the concept of an asymptotically \({\Phi}\)-nonexpansive operator. In addition, we establish some Krasnoselskiitype fixed point theorems for the sum of two operators A and B, where the operator A is assumed to be (ws)-compact, and B is a (ws)-compact and asymptotically \({\Phi}\)-nonexpansive operator on an unbounded closed convex subset of a Banach space. Also we present Leray–Schauder alternatives and Furi–Pera-type fixed point theorems for the sum of two (ws)-compact mappings.     

Efficient synthesis of fluorophosphonylated alkyles by ring-opening reaction of cyclic sulfates

Ring-opening reactions of functionalized 1,2-cyclic sulfates and oxetanes with the phosphonodifluoromethyl carbanion are reported. This approach allows an easy access to fluorinated beta-hydroxyphosphonates that are building blocks in the synthesis of acyclic nucleosides. Synthesis of precursors of nucleoside phosphorylase inhibitors from these alcohols is described.     

A dimeric copper coumarin complex: synthesis and crystal structure of [{Cu(4-methyl-7-(salicylideneamino)coumarin)2}2]

A binuclear copper complex [{Cu(L)₂}₂], C₆₈H₄₈Cu₂N₄O₁₂C (where L is 4-methyl-7-(salicylideneamino)coumarin), has been synthesized and characterized using elemental analysis, molar conductance measurements, and infrared, ultraviolet and ESR spectrosopy. The molecular structure of title compound, determined by single-crystal X-ray diffraction studies, reveals that the two symmetric Cu(L)2 units are associated into a dimer by rather long Cu...O bonds. The Cu(II) ions are bridged via the phenolic oxygen of one of the monomers and have distorted trigonal bipyramidal conformation geometry. Within each monomer the two methylsubstituted coumarin skeletons are trans to one another, but adopt a parallel arrangement with respect to the other monomer. Only half of the complex molecule can be found in the asymmetric unit, Z′ = 0.5, the other half is generated by the symmetry centre.