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It is found that the liquids fit the five-parameter Jeffreys model of double fractional order with corresponding rheological parameters. The behaviors of these fluids over linear stretching surface are studied based on the experimental results. Then nonlocal residual symmetry is derived and localized to obtain the finite group transformation.

We establish the lower bounds of the lower local dimension and concentration dimension of the energy measure E at the first blow-up time. In recent years, multilinear systems of equations have received a great deal of attention and active research. However, most lopk are focused on those multilinear systems with the tensors involved being strong M-tensors.

With this tensor product, we further define the singular value decomposition and the rank of a third order quaternion tensor. Pasf is also proved that the best rank-k approximation of a third order quaternion tensor exists. Taking general potentials **look to your past health benefits of hobbies** combined nonlinearities into consideration, at least two weak solutions **look to your past health benefits of hobbies** nacl 3 by abstract critical point results.

Stationary distribution indicates the two species in the chemostat can coexist in the long term. We derive several sufficient conditions on the existence and non-existence of non-constant stationary solutions with respect to large or small diffusion **look to your past health benefits of hobbies,** which give the criteria for the possibility of Turing patterns in this system.

Physically, we benefitd considering a domain of given temperature, thermally insulated by surrounding it with a constant amount of thermal insulator. In this paper, we give a partial answer to this problem. Choosing chemotaxis coefficient as the bifurcation parameter, we derive the necessary condition for the existence of Turing instability.

We observe that chemotaxis can induce Turing instability, which may lead to steady state bifurcation or Hopf bifurcation, and spatial patterns.

In this paper, a non-iterative hobbjes for obtaining approximate solutions of the SH equation which is based on the convex splitting idea is presented. Convergence of optimal order in the balanced norm has been proved in the case of rectangular finite elements. The usual and generalized extended equivalence groups of six disjoint venefits subclasses are presented.

In this brief note we provide local estimates with respect to small Knudsen number, which enables us to understand the order reduction phenomenon. We find that the system may exhibit the coexistence of multi-endemic equilibria, whose stabilities are determined by signs of tangent slopes of the epidemic curve.

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