Fusion and fission solitons for the (2+1)-dimensional generalized Breor-Kaup system

With a projective equation and a linear variable separation method, this paper derives new families of variable separation solutions （including solitory wave solutions, periodic wave solutions, and rational function solutions） with arbitrary functions for （2＋1）-dimensional generalized Breor-Kaup （GBK） system. Based on the derived solitary wave excitation, it obtains fusion and fission solitons.

Data-driven fusion and fission solutions in the Hirota–Satsuma–Ito equation via the physics-informed neural networks method

Fusion and fission are two important phenomena that have been experimentally observed in many real physical models.In this paper,we investigate the two phenomena in the(2+1)-dimensional Hirota-Satsuma-Ito equation via the physics-informed neural networks(PINN)method.By choosing suitable physically constrained initial boundary conditions,the data-driven fusion and fission solutions are obtained for the first time.Dynamical behaviors and error analysis of these solutions are investigated via illustratively numerical figures,which show that good results are achieved.It is pointed out that the PINN method adopted here can be effectively used to construct the data-driven fusion and fission solutions for other nonlinear integrable equations.Based on the powerful predictive capability of the PINN method and wide applications of fusion and fission in many physical areas,it is hoped that the data-driven solutions obtained here will be helpful for experts to predict or explain related physical phenomena.

Altered synaptic currents,mitophagy,mitochondrial dynamics in Alzheimer's disease models and therapeutic potential of Dengzhan Shengmai capsules intervention

Emerging research suggests a potential association of progression of Alzheimer's disease(AD)with alterations in synaptic currents and mitochondrial dynamics.However,the specific associations between these pathological changes remain unclear.In this study,we utilized Aβ42-induced AD rats and primary neural cells as in vivo and in vitro models.The investigations included behavioural tests,brain magnetic resonance imaging(MRI),liquid chromatography-tandem mass spectrometry(UPLC-MS/MS)analysis,Nissl staining,thioflavin-S staining,enzyme-linked immunosorbent assay,Golgi-Cox staining,transmission electron microscopy(TEM),immunofluorescence staining,proteomics,adenosine triphosphate(ATP)detection,mitochondrial membrane potential(MMP)and reactive oxygen species(ROS)assessment,mitochondrial morphology analysis,electrophysiological studies,Western blotting,and molecular docking.The results revealed changes in synaptic currents,mitophagy,and mitochondrial dynamics in the AD models.Remarkably,intervention with Dengzhan Shengmai(DZSM)capsules emerged as a pivotal element in this investigation.Aβ42-induced synaptic dysfunction was significantly mitigated by DZSM intervention,which notably amplified the frequency and amplitude of synaptic transmission.The cognitive impairment observed in AD rats was ameliorated and accompanied by robust protection against structural damage in key brain regions,including the hippocampal CA3,primary cingular cortex,prelimbic system,and dysgranular insular cortex.DZSM intervention led to increased IDE levels,augmented long-term potential(LTP)amplitude,and enhanced dendritic spine density and length.Moreover,DZSM intervention led to favourable changes in mitochondrial parameters,including ROS expression,MMP and ATP contents,and mitochondrial morphology.In conclusion,our findings delved into the realm of altered synaptic currents,mitophagy,and mitochondrial dynamics in AD,concurrently highlighting the therapeutic potential of DZSM intervention.

Dimensional Analysis and Similarity Method Driving Self-similar Solutions of the First and Second Kind Inducing Energy

Nearly all scientists,at conjunction with simplifying a differential equation,have probably used dimensional analysis.Dimensional analysis(also called the Factor-Label Method or the Unit Factor Method)is an approach to the problem that uses the fact that one can multiply any number or expression without changing its value.This is a useful technique.However,the reader should take care to understand that chemistry is not simply a mathematics problem.In every physical problem,the result must match the real world.In physics and science,dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions.The dimension of a physical quantity is the combination of the fundamental physical dimensions(usually mass,length,time,electric charge,and temperature)which describe it;for example,speed has the dimension length/time,and may be measured in meters per second,miles per hour,or other units.Dimensional analysis is necessary because a physical law must be independent of the units used to measure the physical variables in order to be general for all cases.One of the most derivation elements from dimensional analysis is scaling and consequently arriving at similarity methods that branch out to two different groups namely self-similarity as the first one,and second kind that through them one can solve the most complex none-linear ODEs(Ordinary Differential Equations)and PDEs(Partial Differential Equations)as well.These equations can be solved either in Eulearian or Lagrangian coordinate systems with their associated BCs(Boundary Conditions)or ICs(Initial Conditions).Exemplary ODEs and PDEs in the form of none-linear can be seen in strong explosives or implosives scenario,where the results can easily be converted to induction of energy in a control forms for a peaceful purpose(i.e.,fission or fusion reactions).