Exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with internal controls

For 1‐D first order quasilinear hyperbolic systems without zero eigenvalues, based on the theory of exact boundary controllability of nodal profile, using an extension method, the exact controllability of nodal profile can be realized in a shorter time by means of additional internal controls acting on suitably small space‐time domains. On the other hand, using a perturbation method, the exact controllability of nodal profile for 1‐D first order quasilinear hyperbolic systems with zero eigenvalues can be realized by additional internal controls to the part of equations corresponding to zero eigenvalues. Furthermore, by adding suitable internal controls to all the equations on suitable domains, the exact controllability of nodal profile for systems with zero eigenvalues can be realized in a shorter time.     

A regularized trace formula and oscillation of eigenfunctions of a Sturm‐Liouville operator with retarded argument at 2 points of discontinuity

In this study, first, a formula for regularized sums of eigenvalues of a Sturm‐Liouville problem with retarded argument at 2 points of discontinuity which contains a spectral parameter in the boundary conditions is obtained. After that, oscillation properties of the related problem is investigated. Finally, under the condition that a subset of nodal points is dense in definition set, the potential function is determined.     

On the Rational Drug Design for Hypertension through NMR Spectroscopy

Antagonists of the AT1receptor (AT1R) are beneficial molecules that can prevent the peptide hormone angiotensin II from binding and activating the specific receptor causing hypertension in pathological states. This review article summarizes the multifaced applications of solid and liquid state high resolution nuclear magnetic resonance (NMR) spectroscopy in antihypertensive commercial drugs that act as AT1R antagonists. The 3D architecture of these compounds is explored through 2D NOESY spectroscopy and their interactions with micelles and lipid bilayers are described using solid state ¹³CP/MAS, ³¹P and ²H static solid state NMR spectroscopy. Due to their hydrophobic character, AT1R antagonists do not exert their optimum profile on the AT1R. Therefore, various vehicles are explored so as to effectively deliver these molecules to the site of action and to enhance their pharmaceutical efficacy. Cyclodextrins and polymers comprise successful examples of effective drug delivery vehicles, widely used for the delivery of hydrophobic drugs to the active site of the receptor. High resolution NMR spectroscopy provides valuable information on the physical-chemical forces that govern these drug:vehicle interactions, knowledge required to get a deeper understanding on the stability of the formed complexes and therefore the appropriateness and usefulness of the drug delivery system. In addition, it provides valuable information on the rational design towards the synthesis of more stable and efficient drug formulations.     

Phytochemical and Biological Evaluation of a Newly Designed Nutraceutical Self-Nanoemulsifying Self-Nanosuspension for Protection and Treatment of Cisplatin Induced Testicular Toxicity in Male Rats

The incorporation of cisplatin (CP) as a cytotoxic antineoplastic agent in most chemotherapeutic protocols is a challenge due to its toxic effect on testicular tissues. Natural compounds present a promising trend in research, so a new nutraceutical formulation (NCF) was designed to diminish CP spermatotoxicity. A combination of three nutraceutical materials, 250 mg Spirulina platensis powder (SP), 25 mg Tribulus terrestris L. extract (TT), and 100 mg fish oil (FO) were formulated in self-nanoemulsifying self-nanosuspension (SNESNS). SP was loaded into the optimized self-nanoemulsifying system (30% FO, 50% span 80/cremophor EL and 20% isopropanol) and mixed with TT aqueous solution to form SNESNS. For the SP, phytochemical profiling revealed the presence of valuable amounts of fatty acids (FAs), amino acids, flavonoids, polyphenols, vitamins, and minerals. Transmission electron microscopy (TEM) and particle size analysis confirmed the formation of nanoemulsion-based nanosuspension upon dilution. Method validation of the phytochemical constituents in NCF has been developed. Furthermore, NCF was biologically evaluated on male Wistar rats and revealed the improvement of spermatozoa, histopathological features, and biochemical markers over the CP and each ingredient group. Our findings suggest the potential of NCF with SNESNS as a delivery system against CP-induced testicular toxicity in male rats.     

Solubility and Stability of Some Pharmaceuticals in Natural Deep Eutectic Solvents-Based Formulations

Some medicines are poorly soluble in water. For tube feeding and parenteral administration, liquid formulations are required. The discovery of natural deep eutectic solvents (NADES) opened the way to potential applications for liquid drug formulations. NADES consists of a mixture of two or more simple natural products such as sugars, amino acids, organic acids, choline/betaine, and poly-alcohols in certain molar ratios. A series of NADES with a water content of 0–30% (w/w) was screened for the ability to solubilize (in a stable way) some poorly water-soluble pharmaceuticals at a concentration of 5 mg/mL. The results showed that NADES selectively dissolved the tested drugs. Some mixtures of choline-based NADES, acid-neutral or sugars-based NADES could dissolve chloral hydrate (dissociated in water), ranitidine·HCl (polymorphism), and methylphenidate (water insoluble), at a concentration of up to 250 mg/mL, the highest concentration tested. Whereas a mixture of lactic-acid–propyleneglycol could dissolve spironolacton and trimethoprim at a concentration up to 50 and 100 mg/mL, respectively. The results showed that NADES are promising solvents for formulation of poorly water-soluble medicines for the development of parenteral and tube feeding administration of non-water-soluble medicines. The chemical stability and bioavailability of these drug in NADES needs further studies.     

Severi varieties on blow-ups of the symmetric square of an elliptic curve

We prove that certain Severi varieties of nodal curves of positive genus on general blow-ups of the twofold symmetric product of a general elliptic curve are nonempty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces.     

Solvability of the fractional hyperbolic Keller–Segel system

We study a new nonlocal approach to the mathematical modelling of the chemotaxis problem, which describes the random motion of a certain population due to a substance concentration. Considering the initial–boundary value problem for the fractional hyperbolic Keller–Segel model, we prove the solvability of the problem. The solvability result relies mostly on fractional calculus and kinetic formulation of scalar conservation laws.     

Instability Entanglement in the Electron Cyclotron Maser

Investigation of absolute instability (AI) and convective instability (CI) of the electron cyclotron maser has independently led to the birth of gyrotron oscillators and amplifiers. Here, it is demonstrated that these instabilities can form a cooperative relationship owing to the nonlinear behavior of the stimulated electron beam. The CI can be induced in a zero-drive system with the assistance of AI, and the ohmic losses of all the excited waves inside the system are greatly reduced, which is called “instability entanglement” here. According to the theoretical and experimental study of a 167/330 GHz gyrotron, when instability entanglement occurs, the ohmic dissipation decreases to one-ninth of the AI-only condition, and the output power is enhanced by 20%. This discovery is promising for surpassing the ceiling of output power and frequency of gyrodevices placed by ohmic losses.     

弹性力学的混合方程和Hamilton正则方程

本文指出,在弹性力学基本方程中,按变量分类的位移方程,应力方程以外的第三种混合方程,以及按运算子分类的微分方程、变分原理以外的第三种Hamilton方程,它们正好是对应的。本文讨论了静力的和动力的情况以及它们可能的应用。     

高维线性插值方法及其在3维温度场计算中的应用

通过分析1维和2维线性插值可以推导出任意斜角直线坐标系下n维线性插值的一般计算公式以及有唯一解的条件,这一结论能够应用于三维温度场计算。可以将n维插值问题归结如下:已知n 1维空间中的n 1个点的坐标以及第n 2个点的n个坐标分量xn 2,1,x n 2,2,,xn 2,n,求解该点的第n 1个坐标分量xn 2,n 1。根据线性插值定义,第n 2个点位于前n 1个点所确定的n维超平面上。根据这一条件列写方程、求解方程可得到插值xn 2,n 1。n维插值问题有唯一解的条件是已知的n 1个点在n维空间中构成的多面体的体积不为0。推导过程在斜角直线坐标系中完成,因而结论具有较大普适性。