Abundant different types of exact soliton solution to the (4+1)-dimensional Fokas and (2+1)-dimensional breaking soliton equations

The prime objective of this paper is to explore the new exact soliton solutions to the higher-dimensional nonlinear Fokas equation and(2+1)-dimensional breaking soliton equations via a generalized exponential rational function(GERF) method. Many different kinds of exact soliton solution are obtained, all of which are completely novel and have never been reported in the literature before. The dynamical behaviors of some obtained exact soliton solutions are also demonstrated by a choice of appropriate values of the free constants that aid in understanding the nonlinear complex phenomena of such equations. These exact soliton solutions are observed in the shapes of different dynamical structures of localized solitary wave solutions, singular-form solitons, single solitons,double solitons, triple solitons, bell-shaped solitons, combo singular solitons, breather-type solitons,elastic interactions between triple solitons and kink waves, and elastic interactions between diverse solitons and kink waves. Because of the reduction in symbolic computation work and the additional constructed closed-form solutions, it is observed that the suggested technique is effective, robust, and straightforward. Moreover, several other types of higher-dimensional nonlinear evolution equation can be solved using the powerful GERF technique.     

Structure-based design and synthesis of acyclic and substituted heterocyclic phosphonates linearly linked to thiazolobenzimidazoles as potent hydrophilic antineoplastic agents

As a contribution to our investigations to develop multidisciplinary entities of substituted heterocycle phosphor esters, in this paper, we prepared a series of thiazolobenzimidazoles incorporating phosphor esters of potential anticancer properties. Phosphoryl reagents were applied on E-3-(N,N-dimethylamino)-1-(3-methythiazolo[3,2-a]benzoimidazol-2-yl)prop-2-en-1-one and 1-(3-methylthiazolo[3,2-a]benzimidazol-2-yl)ethanone. The reactions proceeded under mild conditions to give an ensemble of 14 new phosphonates in good yields (68–74%). The stereoselective chemistry was studied by a series of heteronuclear ¹³C[¹H]-nOe experiments. Based on the prediction studies in the early stage using PASS algorithm 14, the synthesized phosphonates were evaluated as antitumor candidates at a dose of 10 µmol/mL against human breast and human colon tumor (4 cultured cell lines each). Three products showed significant antineoplastic potency in relative to the standard drug, adriamycin. Permeability of the lead molecules was determined and the structure–activity relationship (SAR) was discussed to suggest a pro-drug chromophore. Furthermore, there was good coincidence of experimental data of antitumor properties and prediction results.     

Synthesis and characterization of new pyrazole-based thiazoles

A series of new 5-(heteroaryldiazenyl)thiazole incorporating pyrazole moiety have been synthesized through coupling of the thiazole with the appropriate heteroaryldiazonium salts. The newly synthesized compounds were characterized by elemental analysis, spectroscopic (IR, ¹H NMR, and Mass) data, and alternative synthesis whenever possible.     

On a method for solving a two-dimensional nonlinear integral equation of the second kind

In this article, the existence of at least one solution of a nonlinear integral equation of the second kind is proved. The degenerate method is used to obtain a nonlinear algebraic system, where the existence of at least one solution of this system is discussed. Finally, computational results with error estimates are obtained using Maple software.     

Visible-light generation of the naked 12-electron fragment C5H5Fe+: alkyne-to-vinylidene isomerization and synthesis of polynuclear iron vinylidene and alkynyl complexes including hexairon stars

Visible-light photolysis of [FeCp(η(6)-C(6)H(5)CH(3))][PF(6)] using a simple 100-W bulb or a compact fluorescent light bulb in the presence of terminal alkynes and dppe yielded the vinylidene complexes [FeCp(═C═CHR)(dppe)][PF(6)] that were deprotonated by t-BuOK to yield the alkynyl complexes [FeCp(-C≡CR)(dppe)]. The reaction has been extended to the synthesis of bis-, tris, tetra-, and hexanuclear iron complexes including three alkynes of the ferrocenyl family.     

Control over the oxidative reactivity of metalloporphyrins. Efficient electrosynthesis of meso,meso-linked zinc porphyrin dimer

The electrochemical oxidation of zinc(II) 5,15-p-ditolyl-10-phenylporphyrin at its first oxidation potential leads to the formation of the corresponding meso-meso porphyrin dimer as the main product. The number of electrons abstracted, the addition of the hindered base 2,6-lutidine as well as operating in DMF, instead of a CH(2)Cl(2)/CH(3)CN mixture are the key parameters to obtain high yields of the desired coupling product. Indeed, when the electrolyses are carried out in the CH(2)Cl(2)/CH(3)CN mixture, the unexpected zinc(II) 5-chloro-10,20-p-ditolyl-15-phenyl porphyrin is produced as a by-product, the chlorine atom originating from the CH(2)Cl(2) solvent. The monomer and the dimer are characterised by electrochemical analysis. The signature of the dimer is clearly distinguished on the cyclic voltammogram of the monomer on condition of the prior addition of 2,6-lutidine as a hindered base, indicating that the dimerisation process is thus strongly accelerated. Besides, unprecedented X-ray crystallographic structures of the monomer and the meso-meso dimer are presented and their respective structural parameters are compared.     

Triaryl-1,3,5-triazinane-2,4,6-triones (Isocyanurates) Peripherally Functionalized by Donor Groups: Synthesis and Study of Their Linear and Nonlinear Optical Properties

The linear optical (LO) and nonlinear optical (NLO) properties of a series of isocyanurates functionalized by donor arms at the periphery are reported herein. These octupolar derivatives were obtained in a straightforward way from commercial isocyanate derivatives and were fully characterized. Although several of these compounds are known, those that exhibited the largest NLO activities are all new compounds. In terms of second-order activity, several of these derivatives exhibit remarkable activity/transparency tradeoffs. In terms of third-order activity, the longer derivatives with the stronger donor groups (X=NH(2) , NMe(2) , or NPh(2) ) were shown to possess significant two-photon absorption cross sections. These strongly luminescent derivatives exhibit two-photon absorption cross sections up to 410?GM. DFT computations were also conducted to unravel their electronic structures and to rationalize their NLO properties. To our knowledge, the present study is the first concerned with the nonlinear optical properties of these original cyclotrimers.     

250 W single-crystal fiber Yb:YAG laser

We demonstrate an Yb:YAG single-crystal fiber laser with 251 W output power in continuous-wave and an optical efficiency of 44%. This performance can be explained by the high overlap between pump and signal beams brought by the pump guiding and by the good thermal management provided by the single-crystal fiber geometry. The oscillator performance with a reflectivity of the output coupler as low as 20% also shows high potential for power amplification.     

Toeplitz matrix method and nonlinear integral equation of Hammerstein type

The existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated.