Approximate controllability of semilinear system involving state-dependent delay via fundamental solution

This article studies approximate controllability for a new class of semilinear control systems involving state-dependent delay in Hilbert space setting. We formulate some new sufficient conditions which ensure the existence of mild solution for the considered system via the Schauder fixed point theorem. We use the theory of fundamental solution and fractional powers of operator, to establish our major results. At last, two examples are constructed to substantiate the application of obtained results.     

Optimal controls for second-order stochastic differential equations driven by mixed-fractional Brownian motion with impulses

We study optimal control problems for a class of second-order stochastic differential equation driven by mixed-fractional Brownian motion with non-instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an example.     

On commutator of generalized Aluthge transformations and Fuglede–Putnam theorem

Let \(A=U|A|\) be the polar decomposition of A on a complex Hilbert space \({\mathscr {H}}\) and \(0<s,t\). Then \({\widetilde{A}}_{s, t}=|A|^sU|A|^t\) and \({\widetilde{A}}_{s, t}^{(*)}=|A^*|^sU|A^*|^t\) are called the generalized Aluthge transformation and generalized \(*\)-Aluthge transformation of A, respectively. A pair (A, B) of operators is said to have the Fuglede–Putnam property (breifly, the FP-property) if \(AX=XB\) implies \(A^*X=XB^*\) for every operator X. We prove that if (A, B) has the FP-property, then \(({\widetilde{A}}_{s, t},{\widetilde{B}}_{s, t})\) and \((({\widetilde{A}}_{s, t})^{*},({\widetilde{B}}_{s, t})^{*})\) has the FP-property for every \(s,t>0\) with \(s+t=1\). Also, we prove that \(({\widetilde{A}}_{s, t},{\widetilde{B}}_{s, t})\) has the FP-property if and only if \((({\widetilde{A}}_{s, t})^{*},({\widetilde{B}}_{s, t})^{*})\) has the FP-property, where A, B are invertible and \( 0 < s, t \) with \( s + t =1\). Moreover, we prove that if \(0 < s, t\) and \({\widetilde{A}}_{s, t}\) is positive and invertible, then \(\left\| {\widetilde{A}}_{s, t}X-X{\widetilde{A}}_{s, t}\right\| \le \left\| A\right\| ^{2t}\left\| ({\widetilde{A}}_{s, t})^{-1}\right\| \left\| X\right\| \) for every operator X. Also, if \( 0 <s, t\) and X is positive, then \(\left\| |{\widetilde{A}}_{s, t}|^{2r} X-X|{\widetilde{A}}_{s, t}|^{2r}\right\| \le \frac{1}{2}\left\| |A|\right\| ^{2r}\left\| X\right\| \) for every \(r>0\).     

Semi-batch control over functional group distributions in thermoresponsive microgels

Thermosensitive poly(N-isopropylacrylamide-co-methacrylic acid) (poly(NIPAM-co-MAA)) microgels were prepared via semi-batch free radical copolymerization in which the functional monomer (methacrylic acid) was continuously fed into the reaction vessel at various speeds. Microgels with the same bulk MAA contents (and thus the same overall compositions) but different radial functional group distributions were produced, with batch copolymerizations resulting in core-localized functional groups, fast-feed semi-batch copolymerizations resulting in near-uniform functional group distributions, and slow-feed semi-batch copolymerizations resulting in shell-localized functional groups. Functional group distributions in the microgels were probed using titration analysis, electrophoresis, and transmission electron microscopy. The induced functional group distributions have particularly significant impacts on the pH-induced swelling and cationic drug binding behavior of the microgels; slower monomer feeds result in increased pH-induced swelling but lower drug binding. This work suggests that continuous semi-batch feed regimes can be used to synthesize thermoresponsive microgels with well-defined internal morphologies if an understanding of the relative copolymerization kinetics of each comonomer relative to NIPAM is achieved.     

Hypersensitivity in the 4f–4f absorption spectra of tris (acetylacetonato) neodymium(III) complexes with imidazole and pyrazole in non-aqueous solutions. Effect of environment on hypersensitive transitions

The optical absorption spectra of [Nd(acac)₃(H₂O)₂]·H₂O, [Nd(acac)₃(im)₂] and [Nd(acac)₃(pz)₂] (where acac is the anion of acetylacetone, im is imidazole and pz is pyrazole) complexes in the visible region have been analyzed. The transition ⁴G_5/2←⁴I_9/2 located near the middle of the visible region (17,500 cm^?1) is hypersensitive. Its behavior is in sharp contrast to many other typically weak and consistently unvaried, normal 4f–4f transitions. It is overlapped by a less intense transition ²G_7/2←⁴I_9/2. The band shapes of the hypersensitive transition show remarkable changes on passing from aqueous solution to various non-aqueous solutions, which is the result of changes in the environment about the Nd(III) ion in the various solutions and suggests coordination of a solvent molecules. Pyridine has been found especially effective in promoting 4f–4f electric-dipole intensity. The DMSO invades the complexes and replaces the water molecules and heterocyclic amines from the coordination sphere. Two DMSO molecules coordinate and the complexes acquire similar structure, [Nd(acac)₃(DMSO)₂] in solution. The oscillator strength and the band shape of the hypersensitive transition of all the complexes remains the same in this solvent. The IR spectra and the NMR spectra of the complexes have also discussed.     

Variation in minerals, phenolics and antioxidant activity of peel and pulp of different varieties of peach (Prunus persica L.) fruit from Pakistan

Peach (Prunus persica L.), being a potential source of bioactive compounds, has been demonstrated to have medicinal benefits. In this study variation of minerals and antioxidant characteristics (total phenolic contents, total flavonoid contents, reducing power, inhibition of peroxidation using linoleic acid system and DPPH free radical scavenging activity) between peel and pulp parts of different peach varieties, namely Golden, Shireen, and Shahpasand were investigated. The peel and pulp extracts, derived from the varieties analyzed, exhibited an appreciable amount of total phenolics (TP) and total flavonoids (TF), ranging from 1,209.3-1,354.5, 711.7-881.3 mg GAE/100 g and 599.7-785.5, 301.3-499.7 mg CE/100 g on a dry weight basis, respectively. Reducing power of peel and pulp extracts (12.5 mg/mL concentration) ranged from 2.57-2.77 and 1.54-1.99.The inhibition of linoleic acid peroxidation and DPPH scavenging activity of the extracts varied from 70.8-80.9% and 66.8-76.5% in peels, and 51.9-60.1% and 43.4-49.1% in pulps. The mineral analysis revealed that the content of K was highest in both parts of the peach fruit followed by Mg, Ca, Fe, Mn and Zn. The results of our present study indicate that peach peel had significantly higher levels of minerals, antioxidant capacity and phenolics than those of the pulp, suggesting the intake of unpeeled peach as a potential source of high-value components. The peach peel can be a useful as a viable source of natural antioxidants for functional foods and nutraceutical applications.     

Improvement in the Water Retention Characteristics of Sandy Loam Soil Using a Newly Synthesized Poly(acrylamide-<em>co</em>-acrylic Acid)/AlZnFe₂O₄ Superabsorbent Hydrogel Nanocomposite Material

The use of some novel and efficient crop nutrient-based superabsorbent hydrogel nanocomposites (SHNCs), is currently becoming increasingly important to improve the crop yield and productivity, due to their water retention properties. In the present study a poly(Acrylamide-co-acrylic acid)/AlZnFe₂O₄ superabsorbent hydrogel nanocomposite was synthesized and its physical properties characterized using Energy Dispersive X-ray (EDX), FE-SEM and FTIR spectroscopic techniques. The effects of different levels of SHNC were studied to evaluate the moisture retention properties of sandy loam soil (sand 59%, silt 21%, clay 19%, pH 7.4, EC 1.92 dS/m). The soil amendment with 0.1, 0.2, 0.3 and 0.4 w/w% of SHNC enhanced the moisture retention significantly at field capacity compared to the untreated soil. Besides, in a separate experiment, seed germination and seedling growth of wheat was found to be notably improved with the application of SHNC. A delay in wilting of seedlings by 5-8 days was observed for SHNC-amended soil, thereby improving wheat plant growth and establishment.     

Multi-dimensional instability of electrostatic solitary waves in ultra-relativistic degenerate electron-positron-ion plasmas

The basic features and multi-dimensional instability of electrostatic (EA) solitary waves propagating in an ultra-relativistic degenerate dense magnetized plasma (containing inertia-less electrons, inertia-less positrons, and inertial ions) have been theoretically investigated by reductive perturbation method and small-k perturbation expansion technique. The Zakharov-Kuznetsov (ZK) equation has been derived, and its numerical solutions for some special cases have been analyzed to identify the basic features (viz. amplitude, width, instability, etc.) of these electrostatic solitary structures. The implications of our results in some compact astrophysical objects, particularly white dwarfs and neutron stars, are briefly discussed.     

Minimizing correlation effect using zero cross correlation code in spectral amplitude coding optical code division multiple access

The use of minimal multiple access interference (MAI) in code design is investigated. Applying a projection and mapping techniques, a code that has a zero cross correlation (ZCC) between users in optical code division multiple access (OCDMA) is presented in this paper. The system is based on an incoherent light source—LED, spectral amplitude coding (SAC), and direct detection techniques at the receiver. Using power spectral density (PSD) function and Gaussian approximation, we obtain the signal-to-noise ratio (SNR) and the bit-error rate (BER) to measure the code performance. Making a comparison with other existing codes, e.g., Hadamard, MFH and MDW codes, we show that our code performs better at BER 10⁻⁹ in terms of number of simultaneous users. We also demonstrate the comparison between the theoretical and simulation analyses, where the results are close to one another.