Involutions of Complexified Quaternions and Split Quaternions

An involution or anti-involution is a self-inverse linear mapping. Involutions and anti-involutions of real quaternions were studied by Ell and Sangwine [15]. In this paper we present involutions and antiinvolutions of biquaternions (complexified quaternions) and split quaternions. In addition, while only quaternion conjugate can be defined for a real quaternion and split quaternion, also complex conjugate can be defined for a biquaternion. Therefore, complex conjugate of a biquaternion is used in some transformations beside quaternion conjugate in order to check whether involution or anti-involution axioms are being satisfied or not by these transformations. Finally, geometric interpretations of real quaternion, biquaternion and split quaternion involutions and anti-involutions are given.     

SOME GEOMETRIC PROPERTIES OF A NEW DIFFERENCE SEQUENCE SPACE INVOLVING LACUNARY SEQUENCES

In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.     

Homogenization and correctors for monotone problems in cylinders of small diameter

In this paper we study the homogenization of monotone diffusion equations posed in an N  -dimensional cylinder which converges to a (one-dimensional) segment line. In other terms, we pass to the limit in diffusion monotone equations posed in a cylinder whose diameter tends to zero, when simultaneously the coefficients of the equations (which are not necessarily periodic) are also varying. We obtain a limit system in both the macroscopic (one-dimensional) variable and the microscopic variable. This system is nonlocal. From this system we obtain by elimination an equation in the macroscopic variable which is local, but in contrast with usual results, the operator depends on the right-hand side of the equations. We also obtain a corrector result, i.e. an approximation of the gradients of the solutions in the strong topology of the space L^p$L^p$ in which the monotone operators are defined.     

The effect of H2O on the sulfation of Havelock limestone under oxy-fuel conditions in a thermogravimetric analyser

A gas mixture representing oxy-fuel combustion conditions was employed in a thermogravimetric analyser to determine the effect of water vapor and SO₂ concentration on limestone sulfation kinetics over the temperature range of 800 to 920 °C. Here, experiments used small samples of particles (4 mg), with small particle sizes (d_p < 38 µm) and large gas flow rates (120 mL/min@NTP) in order to minimize mass transfer interferences. The gas mixture contained 5000 ppm_v SO₂, 2% O₂, and the H₂O content was changed from 0% to 25% with the balance CO₂. When water vapor was added to the gas mixture at lower temperatures (800–870 °C), the limestone SO₂ capture efficiency increased. However, as the temperature became higher, the enhancement in total conversion values decreased. As expected, Havelock limestone at higher temperatures (890 °C, 920 °C, and 950 °C) experienced indirect sulfation and reacted at a faster rate than for lower temperatures (800–870 °C) for direct sulfation over the first five minutes of reaction time. However, the total conversion of Havelock limestone for direct sulfation was generally greater than for indirect sulfation.     

The effect of concrete slab–rockfill interface behavior on the earthquake performance of a CFR dam

Earthquake response of the concrete slab is mostly depended upon its conjunction with rockfill. This study aims to reveal the effect of concrete slab–rockfill interface behavior on the earthquake performance of a concrete-faced rockfill dam considering friction contact and welded contact. Friction contact is provided by using interface elements with five numbers of shear stiffness values. 2D finite element model of Torul concrete-faced rockfill dam is used for this purpose. Linear and materially non-linear time-history analyses considering dam–reservoir interaction are performed using ANSYS. Reservoir water is modeled using fluid finite elements by the Lagrangian approach. The Drucker–Prager model is preferred for concrete slab and rockfill in non-linear analyses. Horizontal component of 1992 Erzincan earthquake with peak ground acceleration of 0.515g is used in analyses. The maximum and minimum displacements and principal stresses are shown by the height of the concrete slab and earthquake performance of the dam is investigated considering different joint conditions for empty and full reservoir cases. In addition, potential damage situations of concrete slab are evaluated.     

Investigation of Yeast Invertase Immobilization onto Cupric Ion-Chelated,Porous, and Biocompatible Poly(Hydroxyethyl Methacrylate-<Emphasis Type="Italic">n</Emphasis>-Vinyl Imidazole) Microspheres

Cupric ion-chelated poly(hydroxyethyl methacrylate-n-vinyl imidazole) (poly(HEMA-VIM)) microspheres prepared by suspension polymerization were investigated as a specific adsorbent for immobilization of yeast invertase in a batch system. They were characterized by scanning electron microscopy, surface area, and pore size measurements. They have spherical shape and porous structure. The specific surface area of the p(HEMA-VIM) spheres was found to be 81.2 m²/g with a size range of 70–120 μm in diameter, and the swelling ratio was 86.9%. Then, Cu(II) ion chelated on the microspheres (546 μmol Cu(II)/g), and they were used in the invertase adsorption. Maximum invertase adsorption was 51.2 mg/g at pH 4.5. Cu(II) chelation increases the tendency from Freundlich-type to Langmuir-type adsorption model. The optimum activity for both free and adsorbed invertase was observed at pH 4.5. The optimum temperature for the poly(HEMA-VIM)/Cu(II)-invertase system was found to be at 55 °C, 10 °C higher than that of the free enzyme at 45 °C. V _max values were determined as 342 and 304 U/mg enzyme, for free and adsorbed invertase, respectively. K _m values were found to be same for free and adsorbed invertase (20 mM). Thermal and pH stability and reusability of invertase increased with immobilization.     

Multivariate Optimization and Validation of a CE method for Simultaneous Analysis of Dorzolamide Hydrochloride and Timolol Maleate in Ophthalmic Solution

A fast, accurate, precise, and sensitive capillary electrophoretic method has been developed for simultaneous analysis of dorzolamide hydrochloride and timolol maleate in eye drops. Response-surface methodology with a central composite design was used for optimization of buffer pH, applied potential, and temperature. Capillary electrophoresis at 25??C with NaH₂PO₄ buffer (pH?6.00, 0.025?M), and an applied potential of 20?kV was found to be suitable, and under these optimum conditions, dorzolamide hydrochloride and timolol maleate were separated in approximately 3?min. This method was validated and successfully applied to a pharmaceutical preparation, ophthalmic solution, and the results were compared with those from a spectrophotometric method described in the literature.     

Spectroscopic and structural properties of N-(acetamide) morpholinium bromide

A new crystal of N-(acetamide) morpholinium (NAM) bromide has been prepared in methanol at room temperature and characterized by single crystal X-ray analysis, elemental analysis, GS-MS, FTIR, NMR((1)H,(13)C, DEPTH and HETCOR). The N-(acetamide) morpholinium crystallizes in the orthorhombic crystal system, Pnma with unit cell a=12.798(9) ?, b=7.222(5) ?, c=9.244(5) ?, β=90.00, V=854.4(9) ?(3), Z=4. The X-ray structure determination revealed that there are strong inner and intermolecular hydrogen bonds in the crystal.     

Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control

This paper proposes a new speed and current control scheme for a Permanent Magnet Synchronous Motor (PMSM) by means of a nonlinear and adaptive backstepping design. All the parameters in both PMSM and load dynamics are considered unknown. It is assumed that all state variables are measurable and available for feedback in the controller design. The final control and parameter estimation laws are derived by the design of the virtual control inputs and the Lyapunov function candidate. The overall control system is asymptotically stable according to stability analysis results based on Lyapunov stability theory. Simulation results clearly show that the controller guarantees tracking of a time varying reference speed owing to the fact that the speed and current tracking errors asymptotically converge to zero despite all the parameter uncertainties/perturbations and load torque disturbance variation. Numerical simulations reveal the performance and feasibility of the proposed controller.     

A note on a problem of Abramovich,Aliprantis and Burkinshaw

Let B and T be two positive operators on a Banach lattice such that B is compact-friendly and T is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that T has a non-trivial closed invariant subspace provided B is positively quasi-similar to T. This gives an affirmative answer to a problem of Abramovich, Aliprantis and Burkinshaw with the commutativity condition replaced by the positive quasi-similarity of the corresponding operators. The notion of strong compact-friendliness is also introduced and relevant facts about it are discussed.