Heterocyclic compounds are employed in many applications, and numerous researchers have created liquid crystals by adding heterocyclic to the structures of these molecules. This work includes the synthesis and characterization of new compounds that contain 5H-thiazolo [4,3-b][1,3,4] thiadiazol united in multiple steps, starting with the synthesis of the aldehyde compound [I] by reaction chloro ethyl acetate with 4-hydroxybenzaldehyde in the presence of ethanol and potassium carbonate, followed by reactions with thiosemicarbazide, mercapto acetic acid in sulphuric acid to produce compound [II] then reflux compound [II] with hydrazine hydrate to product compound [III], after that reaction the later compound with nalkoxybenzaldehyde [IV]n and a few drops of piperidine in THF as a solvent to produce new Schiff᾽s-bases compounds contain 5H-thiazolo [4,3-b] [1,3,4] thiadiazol unite [V]n, FTIR and 1HNMR spectroscopy were used to analyze the compounds, a polarized optical microscope (POM) and differential scanning calorimetry (DSC) were used to examine the characteristics of the liquid crystals. In the Smectic A (SmA) and nematic phases, liquid crystal characteristics are present in all compounds [V]n. In addition to the nematic phase, all compounds [V]n showed enantiotropic dimorphism in the SmA phase. It was revealed that compounds [V]n with 5H- thiazole [4,3-b] [1,3,4]thiadiazol unit, the rigid-rod core of Schiff bases, and the formation of a supramolecular hydrogen bond between the derivatives [V]n had liquid crystallinity, depending on the chain length of the alkoxy group as a terminal substituent.
In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.
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In this paper, we are mainly concerned with estimating cascade reliability model (2+1) based on inverted exponential distribution and comparing among the estimation methods that are used . The maximum likelihood estimator and uniformly minimum variance unbiased estimators are used to get of the strengths and the stress ;k=1,2,3 respectively then, by using the unbiased estimators, we propose Preliminary test single stage shrinkage (PTSSS) estimator when a prior knowledge is available for the scale parameter as initial value due past experiences . The Mean Squared Error [MSE] for the proposed estimator is derived to compare among the methods. Numerical results about conduct of the considered
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