Full Symmetry Groups and Exact Solutions towhere , , , , and are functions of (, , ) to be determined by requiring (, , ) to satisfy the same (2+1)- dimensional GKP equation as V(, , ) under the transfor- mation {V, , , } → {, , , }GKP Equations...
With the transformation groups, a type of group invariant solutions of cKdV equation can be derived from a simple one. Furthermore, some transformations from the cKdV equation to KP equation can also be discovered by this method. Editorial remark: There are doubts about a proper peer-reviewing...
For the (2 + 1)-dimensional Broer-Kaup system, we study the corresponding Lie symmetry groups, and obtain the symmetry group theorem and the Backlund transformation formula of solutions finding. At the same time, we find some new exact solutions of the (
Nanocrystals coated with trimethoxysilylpropyl urea and acetate groups were found to bind with high affinity in the cell nucleus. The avidin-biotin interaction, which serves as a model system for ligand-receptor binding, was used to specifically label F-actin filaments with red nanocrystal probes. ...
Understanding of the conditions resulting in the onset of elastic instabili- ties in viscometric shearing flows is now quite advanced4–6, however the same is not true for extension-dominated or "shear-free" flows, which are much more difficult to study under well-controlled and well-defined ...
of microfluidic devices allow fluids to be deformed at high rates while inertia remains low45, and give ready access to regimes of very high elasticityEl = Wi/Reat which elastic instabilities become prevalent3,46,47,48,49,50. Purely elastic instabilities, i.e. those arising when inertial...
(andthedefinitionofanellipticcurveneedstobeabitmoregeneraltoworkforZ2andZ3butI’llleavethisforinterestreading).Solution:Proceedingasthehintsuggests,wehave(x−R/3)3+R(x−R/3)2+S(x−R/3)+T=x3−Rx2+R2x/3−R3/27+Rx2−2R2x/3+R3/9+Sx−RS/3+T=x3+(S−R2/3)x−R3/...
Globalization, the growth of the world population, urbanization and the growth of the volume of the flow of goods have generated numerous problems in city logistics (CL). The opportunity to solve them is found in various fields by defining and implementi
Cyberattacks can compromise the smart grid’s dependability, availability, and privacy. Users, the communication network of smart devices and sensors, and network administrators are the three layers of an innovative grid network vulnerable to cyberattacks. In this study, we look at the many risks ...
Overall, “Groups & Symmetry” by Armstrong is praised for its practical approach to teaching group theory and its applications in the study of symmetry. It’s particularly suitable for those interested in exploring the connections between abstract algebra and real-world phenomena. However, readers ...