They established the existence and uniqueness results and some fundamental differential inequalities for hybrid differential equations initiating the study of theory of such systems and proved utilizing the theory of inequalities, its existence of extremal solutions and a comparison result.
They established the existence, uniqueness results and some fundamental differential inequalities for hybrid differential equations initiating the study of theory of such systems and proved utilizing the theory of inequalities, its existence of extremal solutions and comparison results.
They established the existence and uniqueness results and some fundamental differential inequalities for fractional hybrid differential equations, initiating the study of such systems, and proved, utilizing the theory of inequalities, the existence of extremal solutions and a comparison result.
A five-ratio test utilizing six genes proved to be 100% accurate (26 of 26 samples) for distinguishing benign from malignant bladder tissue samples (P < 10−6).
This is straightforward to prove by utilizing the fact that3 mathbf{v}_{{i_{lk}}}^{H}boldsymbol{Psi}_{j}^{- 1} = frac{tilde{ phi}_{ji_{lk}}}{B} mathbf{v}_{{i_{lk}}}^{H}.
Theorems concerning stationary values of the respective Rayleigh quotients are proved by utilizing the generalized orthogonality relationships for the wet modes of these three kinds of liquid containing tank models.
The fact that symmetry of a spatial parallel mechanism can be directly mapped into the workspace of the end-effector is defined as a strengthened theorem and is proved by utilizing the group theory.
The optical response of this filter to normal-incident and oblique-incident light proves that utilizing the high-order band gaps of PCs is an efficient method to lower the difficulties of fabricating PCs, increase the etching depth of semiconductor materials, and reduce the coupling loss at the interface between optical fibers and PC device.
In addition, it has been proven that utilizing hyperbolic tangent sigmoid in the first layer and logarithmic sigmoid in the second layer will produce better results.
However, it has been proven that utilizing hyperbolic tangent sigmoid (tansig) in the first layer and logarithmic sigmoid (logsig) in the second layer will produce better results.
This study proved that utilizing different technologies allowed for control of sources of potential bias in RNA sequencing: all three platforms used for our study gave the same results.
