Asymptotic behaviour of the minima to a class of optimization problems for differential inclusions

Denoting byS _k (ξ _k ) the set of solutions of the Cauchy problem $\dot x \in F_k (t,x),x(0) = \xi _k $ , fork∈N∪{∞}, we prove that, under appropriate assumptions, the sequence {S _k (ξ _k )} _{k ∈ N} converges toS _∞(∈_∞) in the Kuratowski sense as well as in the Mosco sense. This result together with some facts from Γ-convergence theory are used to prove a result concerning the existence and the asymptotic behavior of the minima to the optimization problem $$\min \int_0^T {[g_k (t,x(t)) + h_k (t,\dot x(t))]} dt + \psi _k (\xi ),x \in S_k (\xi ),\xi \in K$$ withK a compact subset ofR ⁿ .     

Laser induced breakdown spectroscopy surface analysis correlated with the process of nanoparticle production by laser ablation in liquids

Linkage isomerism is the coexistence of iso-compositional molecules or solids differing by connectivity of the metal to a ligand. In a crystalline solid state, the rotation is possible for asymmetric ligands, e.g., for cyanide ligand. Here we report on our observation of a phase transition in anhydrous RbMn[Fe(CN)₆] (nearly stoichiometric) and on the effect of linkage isomerism ensuing our interpretation of the results of Mössbauer study in which we observe the iron spin state crossover among two phases involved into this transition. The anhydrous RbMn[Fe(CN)₆] can be prepared via prolonged thermal treatment (1 week at at 80 °C) of the as-synthesized hydrated RbMn[Fe(CN)₆]·H₂O. The latter compound famous for its charge-transfer phase transition is a precursor in our case. As the temperature is raising above 80 °C (remaining below 100 °C) we observe RbMn[Fe(CN)₆] that inherited its F-43 m symmetry from RbMn[Fe(CN)₆]·H₂O transforming to a phase of the Fm-3 m symmetry. In the latter, more than half of Fe^3?+? ions are in high-spin state. We suggest a plausible way to explain the spin-crossover that is to allow the linkage isomerism by rotation of the cyanide ligands.     

Liquid-liquid extraction and cloud point extraction for spectrophotometric determination of vanadium using 4-(2-pyridylazo)resorcinol

Liquid-liquid extraction (LLE) and cloud point extraction (CPE) of vanadium(V) ternary complexes with 4-(2-pyridylazo)resorcinol (PAR) and 2,3,5-triphenyl-2H-tetrazolum chloride (TTC) were investigated. The optimal conditions for vanadium extraction and spectrophotometric determination were identified. The composition (V: PAR: TTC) of the extracted species was 1:2:3 (optimal conditions; LLE), 2:2:2 (low reagents concentrations; LLE), 1:1:1 (short heating time;CPE), and 1: 1: 1 + 1: 1: 0 (optimal extraction conditions; CPE). LLE, performed in the presence of 1,2-diaminocyclohexane-N,N,N′,N′-tetraacetic acid and NH₄F as masking agents, afforded the sensitive, selective, precise, and inexpensive spectrophotometric determination of vanadium. The absorption maximum, molar absorptivity, limit of detection, and linear working range were 559 nm, 1.95 × 10⁵ dm³ mol^?1 cm^?1,0.7 ng cm^?3, and 2.2–510 ng cm^?3, respectively. The procedure thus developed was applied to the analysis of drinking waters and steels. The relative standard deviations for V(V) determination were below 9.4 % (4–6 × 10^?7 mass %; water samples) and 2.12 % (1–3 mass %; steel samples).     

Phytochemical Constituents and Pharmacological Potential of Tamus communis Rhizomes

Tamus communis L. is a plant distributed in a number of geographical areas whose rhizome has been used for centuries as an anti-inflammatory and analgesic remedy. This review aims to summarize the current knowledge of the chemical composition and biological activity of the extracts or individual compounds of the rhizome. The data for the principal secondary metabolites are systematized: sterols, steroidal saponins, phenanthrenes, dihydrophenanthrenes, etc. Results of biological tests for anti-inflammatory action, cytotoxicity, anticholinesterase effect, and xanthine oxidase inhibition are presented. Some open questions about the therapeutic properties of the plant are also addressed.     

Multielemental determination in some water samples by neutron activation method

A method was developed for the determination of element concentrations in structured water samples (water with high oligoelements content). Sixteen elements (As, Br, Ca, Ce, Co, Cr, Eu, Fe, K, La, Lu, Na, Sb, Sc, Sm, Zn) were determined in 4 structured water samples and one taken from the water tap. The samples were preconcentrated evaporating 1 1 at atmospheric pressure and obtaining 100–500 mg of dry residue. Measurement accuracy by -spectroscopy was 3–30% and it can be improved by increasing the measurement time. The method allows simultaneous multielement analysis of various water sources and may successfully be used in environmental pollution control.     

Dynamics analysis of the Minuteman cover drive

Recursive matrix relations in kinematics and dynamics analysis of a 1-DOF compound planetary gear train are established in the paper. The mechanism of the Minuteman cover drive is a system with four moving links and three gear pairs controlled by one electric motor. Knowing the rotation motion of the output link, the inverse dynamic problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations. Finally, some simulation graphs for the input and output angles of rotation, the torque and the power of the actuator are obtained.     

Small scale velocity jumps in shear turbulence

We measure structure functions and structures in uniformly sheared strong turbulence using an array of hot-wire velocity sensors. We find that the large-scale shear persists down to the smallest scales. There is a marked asymmetry between velocity increments measured in the shear direction, and those measured in the plane perpendicular to it. In the shear direction the scaling exponents tend to a constant, signifying the presence of small-scale cliffs. Direct evidence for those is presented by the spatial structure of the strongest velocity gradients.     

Directionally Continuous Selections and Nonconvex Evolution Inclusions

In Bressan and Staicu, Set-Valued Anal. 2 (1994), 415–437, qualitative properties for solutions of the evolution inclusion Ax+F(t,x), with A generator of a contractive semigroup and F a lower semicontinuous closed valued multifunction defined on compact subset of R×cl(D(A)), were deduced as corollaries of similar properties for solutions of the evolution inclusion Ax+G(t,x), where G is upper semicontinuous compact convex valued, obtained from a suitable directionally continuous selection from F.In this paper we prove that the compactness assumption on the domain of F can be avoided.