Ultrasonic emulsification of parenteral valproic acid-loaded nanoemulsion with response surface methodology and evaluation of its stability

Response surface methodology (RSM) was used to optimize the formulation of a nanoemulsion for central delivery following parenteral administration. A mixture of medium-chain triglyceride (MCT) and safflower seed oil (SSO) was determined as a sole phase from the emulsification properties. Similarly, a natural surfactant (lecithin) and non-ionic surfactant (Tween 80) (ratio 1:2) were used in the formulation. A central composite design (CCD) with three-factor at five-levels was used to optimize the processing method of high energy ultrasonicator. Effects of pre-sonication ultrasonic intensity (A), sonication time (B), and temperature (C) were studied on the preparation of nanoemulsion loaded with valproic acid. Influence of the aforementioned specifically the effects of the ultrasonic processing parameters on droplet size and polydispersity index were investigated. From the analysis, it was found that the interaction between ultrasonic intensity and sonication time was the most influential factor on the droplet size of nanoemulsion formulated. Ultrasonic intensity (A) significantly affects the polydispersity index value. With this optimization method, a favorable droplet size of a nanoemulsion with reasonable polydispersity index was able to be formulated within a short sonication time. A valproic acid loaded nanoemulsion can be obtained with 60% power intensity for 15 min at 60 °C. Droplet size of 43.21 ± 0.11 nm with polydispersity index of 0.211 were produced. The drug content was then increased to 1.5%. Stability study of nanoemulsion containing 1.5% of valproic acid had a good stability as there are no significant changes in physicochemical aspects such as droplet size and polydispersity index. With the characteristisation study of pH, viscosity, transmission electron microscope (TEM) and stability assessment study the formulated nanoemulsion has the potential to penetrate blood–brain barrier in the treatment of epilepsy.     

Convex analysis and financial equilibrium

Convexity has long had an important role in economic theory, but some recent developments have featured it all the more in problems of equilibrium. Here the tools of convex analysis are applied to a basic model of incomplete financial markets in which assets are traded and money can be lent or borrowed between the present and future. The existence of an equilibrium is established with techniques that include bounds derived from the duals to problems of utility maximization. Composite variational inequalities furnish the modeling platform. Models with and without short-selling are handled, moreover in the absence of any requirement that agents must initially have a positive amount of every asset, as is typical in equilibrium work in economics.     

Direct observations of the leaching of a simulated nuclear waste glass in a radiation environment

The durability of the media proposed for the containment of commercial nuclear waste will be affected not only by the differences in groundwater composition that they might encounter but also by the changes that their own irradiation fields will make to these solutions. Experimental results that question the ability of current leaching experiments to predict the stability of nuclear waste composites are presented.     

The Central Curve in Linear Programming

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answering a question of Bayer and Lagarias. These invariants, along with the degree of the Gauss image of the curve, are expressed in terms of the matroid of the input matrix. Extending work of Dedieu, Malajovich and Shub, this yields an instance-specific bound on the total curvature of the central path, a quantity relevant for interior-point methods. The global geometry of central curves is studied in detail.     

Piperazine Functionalization of C70 for Incorporation into Supramolecular Assemblies

The photochemical reaction of piperazine with C₇₀ produces a mono‐adduct (N(CH₂CH₂)₂NC₇₀) in high yield (67 %) along with three bis‐adducts. These piperazine adducts can combine with various Lewis acids to form crystalline supramolecular aggregates suitable for X‐ray diffraction. The structure of the mono‐adduct was determined from examination of the adduct I₂N(CH₂CH₂)₂NI₂C₇₀ that was formed by reaction of N(CH₂CH₂)₂NC₇₀ with I₂. Crystals of polymeric {Rh₂(O₂CCF₃)₄N(CH₂CH₂)₂NC₇₀}_n?nC₆H₆ that formed from reaction of the mono‐adduct with Rh₂(O₂CCF₃)₄ contain a sinusoidal strand of alternating molecules of N(CH₂CH₂)₂NC₇₀ and Rh₂(O₂CCF₃)₄ connected through Rh?N bonds. Silver nitrate reacts with N(CH₂CH₂)₂NC₇₀ to form black crystals of {(Ag(NO₃))₄(N(CH₂CH₂)₂NC₇₀)₄}_n?7nCH₂Cl₂ that contain parallel, nearly linear chains of alternating (N(CH₂CH₂)₂NC₇₀ molecules and silver ions. Four of these {Ag(NO₃)N(CH₂CH₂)₂NC₇₀}_n chains adopt a structure that resembles a columnar micelle with the ionic silver nitrate portion in the center and the nearly non‐polar C₇₀ cages encircling that core. Of the three bis‐adducts, one was definitively identified through crystallization in the presence of I₂ as ¹²{N(CH₂CH₂)₂N}₂C₇₀ with addends on opposite poles of the C₇₀ cage and a structure with C_2v symmetry. In ¹²{I₂N(CH₂CH₂)₂N}₂C₇₀, individual ¹²{I₂N(CH₂CH₂)₂N}₂C₇₀ units are further connected by secondary I2???N2 interactions to form chains that occur in layers within the crystal. Halogen bond formation between a Lewis base such as a tertiary amine and I₂ is suggested as a method to produce ordered crystals with complex supramolecular structures from substances that are otherwise difficult to crystallize.     

Stability analysis and classification of Runge–Kutta methods for index 1 stochastic differential-algebraic equations with scalar noise

The problem of solving stochastic differential-algebraic equations (SDAEs) of index 1 with a scalar driving Wiener process is considered. Recently, the authors have proposed a class of stiffly accurate stochastic Runge–Kutta (SRK) methods that do not involve any pseudo-inverses or projectors for the numerical solution of the problem. Based on this class of approximation methods, classifications for the coefficients of stiffly accurate SRK methods attaining strong order 0.5 as well as strong order 1.0 are calculated. Further, the mean-square stability of the considered class of SRK methods is analyzed. As the main result, families of A-stable efficient order 0.5 and 1.0 stiffly accurate SRK methods with a minimal number of stages for SDEs as well as for SDAEs are presented.     

Synthesis of Structurally Varied 1,3‐Disiloxanediols and Their Activity as Anion‐Binding Catalysts

A series of new 1,3‐disiloxanediols has been synthesized, including naphthyl‐substituted and unsymmetrical siloxanes, and demonstrated as a new class of anion‐binding catalysts. In the absence of anions, diffusion‐ordered spectroscopy (DOSY) displays self‐association of 1,3‐disiloxanediols through hydrogen‐bonding interactions. Binding constants determined for 1,3‐disiloxanediol catalysts indicate strong hydrogen‐bonding and anion‐binding abilities with unsymmetrical siloxanes displaying different hydrogen‐bonding abilities for each silanol group.     

Detection on micro-Doppler effect based on 1550 nm laser coherent radar

A laser coherent detection system of 1550 nm wavelength was presented, and experimental research on detecting micro-Doppler effect in a dynamic target was developed. In this paper, the return signal in the time domain is decomposed into a set of components in different wavelet-scales by multi-resolution analysis, and the components are associated with the vibrational motions in a target. The micro-Doppler signatures are extracted by applying the reconstruction (inverse wavelet transform). During the course of the final data processing frequency analysis and time–frequency analysis are applied to analyze the vibrational signals and estimate the motion parameters successfully. The experimental results indicate that the micro-Doppler information in a moving can be effectively detected, and tiny vibrational signatures also can be acquired effectively by wavelet multi-resolution analysis and time–frequency analysis.