Abstract

  Bivariate time series modeling and forecasting have become a promising field of applied studies in recent times. For this purpose, the Linear Autoregressive Moving Average with exogenous variable ARMAX model is the most widely used technique over the past few years in modeling and forecasting this type of data. The most important assumptions of this model are linearity and homogenous for random error variance of the appropriate model. In practice, these two assumptions are often violated, so the Generalized Autoregressive Conditional Heteroscedasticity (ARCH) and (GARCH) with exogenous varia

A novel series of liquid crystalline compounds containing 2,4-thiazolidinedione units with varying terminal alkyl chain lengths was successfully synthesized and characterized. The chemical structures of the synthesized compounds were confirmed by FT-IR, ¹H-NMR, and mass spectrometry. The mesomorphic behavior was investigated using polarized optical microscopy (POM) and differential scanning calorimetry (DSC). Compounds [V]₄, [V]₅, and [V]₆ exhibited enantiotropic nematic phases, while compound [V]₈ displayed a smectic A (SmA) phase. No liquid crystalline behavior was observed for compound [V]₃. The liquid crystalline properties were found to depend on the terminal-to-lateral chain length ratio, molecular geometry, and the nature

All new compounds synthesized by many reactions starting from a product the compounds [I]a,b from reaction of 3-phenylenediamine or 4-phenylenediamine with chloroacetyl chloride, then the compounds [I]a,b reacted with potassium thiocyanate to yield compounds [II]a,b. While the compounds[III]a,b yield from reacted the compounds [I]a,b with sodium azide then the compounds [III]a,b reacted 1,3-dipolar cycloaddition reaction with acrylic acid to give compounds [IV]a,b and the later compounds reacted with phenylene diamine to product benzimidazole compounds [V]a,b . In addition to synthesized acid chloride compounds [VI]a,b by reacted the compounds [IV]a,b with thionyl chloride .Finally reacted the compounds [VI]a,b with different aromatic amine

In this paper, an ecological model with stage-structure in prey population, fear, anti-predator and harvesting are suggested. Lotka-Volterra and Holling type II functional responses have been assumed to describe the feeding processes . The local and global stability of steady points of this model are established. Finally, the global dynamics are studied numerically to investigate the influence of the parameters on the solutions of the system, especially the effect of fear and anti-predation.