Comparative in vivo constituents and pharmacokinetic study in rats after oral administration of ultrafine granular powder and traditional decoction slices of Chinese Salvia

Salvia miltiorrhiza, one of the most well‐known herbal medicines, is commonly used for the treatment of coronary heart diseases in China. Besides traditional decoction slices (TDS), another relatively new product of S. miltiorrhiza, ultrafine granular powder (UGP; D90 < 45 μm), is also increasingly being used. In this paper, a UHPLC‐LTQ‐Orbitrap MS technique was developed for a metabolite profile study after oral administration of UGP and TDS of S. miltiorrhiza. The results showed that the number of in vivo absorbed compounds from UGP was much greater than that from TDS, and different types of products from S. miltiorrhiza will have different metabolic processes in vivo. Furthermore, a UHPLC‐Q‐Trap MS/MS method for simultaneously determining four tanshinones (tanshinone IIA, dihydrotanshinone I, tanshinone I and cryptotanshinone) was established and applied to assess the pharmacokinetics of the two types of products. All of the analytes displayed significant higher area under the concentration–time curve and peak concentration after oral administration of UGP than after TDS, indicating that ultrafine powder product could improve the bioavailability and absorption of cryptotanshinon,tanshinone II A,dihydrotanshinonE I and tanshinone I in vivo. The present study provides scientific information for further exploration of the pharmacology of these two types of S. miltiorrhiza and offers a reference for clinical administration of S. miltiorrhiza.     

A new class of conformable spectral observers for signal reconstruction

In this work, the design of spectral observers for signal reconstruction based on Kalman filters is performed and evaluated. The conformable derivative and the beta‐derivative were used to design the Kalman filters. Both derivatives satisfy the same formulas of the classical derivation, eg, the chain rule. The derivative order, the Ricatti equation parameters, and the observers tuning parameters were optimized using an optimization algorithm based on the bat's echolocation behavior (Bat algorithm). The simulation results showed the advantages of using the proposed observers for the signal reconstruction.     

Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation

We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.     

Non‐self‐adjoint singular second‐order dynamic operators on time scale

In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.     

Nonexistence of nontrivial global solutions for nonlocal in time differential inequalities

In this paper, some nonlocal in time differential inequalities of Sobolev type are considered. Using the nonlinear capacity method, sufficient conditions for the nonexistence of nontrivial global classical solutions are provided.     

Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.