Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE

In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.

An Efficient Approach for Transforming Unbalanced Transportation Problems into Balanced Problems in Order to Find Optimal Solutions

In operations research, the transportation problem (TP) is among the earliest and most effective applications of the linear programming problem. Unbalanced transportation problems reflect the reality of supply chain and logistics situations where the available supply of goods may not precisely match the demand at different locations. To deal with an unbalanced transportation problem (UTP), it is essential first to convert it into a balanced transportation problem (BTP) to find an initial basic feasible solution (IBFS) and hence the optimal solution. The present paper is concerned with introducing a new approach to convert an unbalanced transportation problem into a balanced one and as a consequence to obtain optimum total transportation cost. Numerical examples are provided to demonstrate the suggested method.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

GLOBAL CLASSICAL SOLUTIONS OF SEMILINEAR WAVE EQUATIONS ON R^(3)×T WITH CUBIC NONLINEARITIES

In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.

Improvement effect of reversible solid solutions Mg_(2)Ni(Cu)/Mg_(2)Ni(Cu)H_(4)on hydrogen storage performance of MgH_(2)

The hydrogen absorption/desorption kinetic properties of MgH_(2)can be effectively enhanced by doping specific catalysts.In this work,MOFs-derived NiCu@C nanoparticles(~15 nm)with regular core-shell structure were successfully prepared and introduced into MgH_(2)(denoted as MgH_(2)-NiCu@C).The onset and peak temperatures of hydrogen desorption of MgH_(2)-11 wt.%NiCu@C are 175.0℃and282.2℃,respectively.The apparent activation energy of dehydrogenated reaction is 77.2±4.5 kJ/mol for MgH_(2)-11 wt.%NiCu@C,which is lower than half of that of the as-milled MgH_(2).Moreover,MgH_(2)-11 wt.%NiCu@C displays great cyclic stability.The strengthening"hydrogen pumping"effect of reversible solid solutions Mg_(2)Ni(Cu)/Mg_(2)Ni(Cu)H_(4)is proposed to explain the remarkable improvement in hydrogen absorption/desorption kinetic properties of MgH_(2).This work offers a novel perspective for the design of bimetallic nanoparticles and beyond for application in hydrogen storage and other energy related fields.

On entire solutions of some Fermat type differential-difference equations

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference equations.On the other hand,we also investigate the existence and growth of solutions of nonlinear differential-difference equations.These results extend and improve some previous in[5,14].

Study of the Relationship Between New Ionic Interaction Parameters and Salt Solubility in Electrolyte Solutions Based on Molecular Dynamics Simulation

Studying the relationship between ionic interactions and salt solubility in seawater has implications for seawater desalination and mineral extraction.In this paper,a new method of expressing ion-to-ion interaction is proposed by using molecular dynamics simulation,and the relationship between ion-to-ion interaction and salt solubility in a simulated seawater water-salt system is investigated.By analyzing the variation of distance and contact time between ions in an electrolyte solution,from both spatial and temporal perspectives,new parameters were proposed to describe the interaction between ions:interaction distance(ID),and interaction time ratio(ITR).The best correlation between characteristic time ratio and solubility was found for a molar ratio of salt-to-water of 10:100 with a correlation coefficient of 0.96.For the same salt,a positive correlation was found between CTR and the molar ratio of salt and water.For type 1-1,type 2-1,type 1-2,and type 2-2 salts,the correlation coefficients between CTR and solubility were 0.93,0.96,0.92,and 0.98 for a salt-to-water molar ratio of 10:100,respectively.The solubility of multiple salts was predicted by simulations and compared with experimental values,yielding an average relative deviation of 12.4%.The new ion-interaction parameters offer significant advantages in describing strongly correlated and strongly hydrated electrolyte solutions.

ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER

In this paper,we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.

New method of local adjuvant therapy with bicarbonate Ringer’s solution for tumoral calcinosis: A case report

BACKGROUND Tumoral calcinosis is a condition characterized by deposits of calcium phosphate crystals in extra-articular soft tissues,occurring in hemodialysis patients.Calcium phosphate crystals are mainly composed of hydroxyapatite,which is highly infilt-rative to tissues,thus making complete resection difficult.An adjuvant method to remove or resolve the residual crystals during the operation is necessary.CASE SUMMARY A bicarbonate Ringer’s solution with bicarbonate ions(28 mEq/L)was used as the adjuvant.After resecting calcium phosphate deposits of tumoral calcinosis as much as possible,while filling with the solution,residual calcium phosphate deposits at the pseudocyst wall can be gently scraped by fingers or gauze in the operative field.A 49-year-old female undergoing hemodialysis for 15 years had swelling with calcium deposition for 2 years in the shoulders,bilateral hip joints,and the right foot.A shoulder lesion was resected,but the calcification remained and early re-deposition was observed.Considering the difficulty of a complete rection,we devised a bicarbonate dissolution method and excised the foot lesion.After resection of the calcified material,the residual calcified material was washed away with bicarbonate Ringer’s solution.CONCLUSION The bicarbonate dissolution method is a new,simple,and effective treatment for tumoral calcinosis in hemodialysis patients.

Using a novel hemostatic peptide solution to prevent bleeding after endoscopic submucosal dissection of a gastric tumor

BACKGROUND Endoscopic mucosal dissection has become the standard treatment for early gastric cancer.However,post-endoscopic submucosal dissection(ESD)ulcer occurs in 4.4%of patients.This study hypothesized whether applying PuraStat,a novel hemostatic peptide solution,prevents post-ESD bleeding.AIM To investigate the preventive potential of PuraStat,a hemostatic formulation,against bleeding in post-ESD gastric ulcers.METHODS Between May 2022 and March 2023,101 patients(Group P)underwent ESD for gastric diseases at our hospital and received PuraStat(2 mL)for post-ESD ulcers.We retrospectively compared this group with a control group(Group C)com-prising 297 patients who underwent ESD for gastric diseases at our hospital between April 2017 and March 2021.P values<0.05 on two-sided tests indicated significance.RESULTS Post-ESD bleeding occurred in 6(5.9%)(95%CI:2.8-12.4)and 20(6.7%)(95%CI:4.4-10.2)patients in Groups P and C,respectively,with no significant between-group difference.The relative risk was 1.01(95%CI:0.95-1.07).The lesser curvature or anterior wall was the bleeding site in all 6 patients who experienced postoperative bleeding in Group P.In multivariate analysis,the odds ratios for resection diameter≥50 mm and oral anticoagulant use were 6.63(95%CI:2.52-14.47;P=0.0001)and 4.04(1.26-0.69;P=0.0164),respectively.The adjusted odds ratio of post-ESD bleeding and PuraStat was 1.28(95%CI:0.28-2.15).CONCLUSION PuraStat application is not associated with post-ESD bleeding.However,the study suggests that gravitational forces may affect the effectiveness of applied PuraStat.

The Extremal Universe Exact Solution from Einstein’s Field Equation Gives the Cosmological Constant Directly

Einstein’s field equation is a highly general equation consisting of sixteen equations. However, the equation itself provides limited information about the universe unless it is solved with different boundary conditions. Multiple solutions have been utilized to predict cosmic scales, and among them, the Friedmann-Lemaître-Robertson-Walker solution that is the back-bone of the development into today standard model of modern cosmology: The Λ-CDM model. However, this is naturally not the only solution to Einstein’s field equation. We will investigate the extremal solutions of the Reissner-Nordström, Kerr, and Kerr-Newman metrics. Interestingly, in their extremal cases, these solutions yield identical predictions for horizons and escape velocity. These solutions can be employed to formulate a new cosmological model that resembles the Friedmann equation. However, a significant distinction arises in the extremal universe solution, which does not necessitate the ad hoc insertion of the cosmological constant;instead, it emerges naturally from the derivation itself. To the best of our knowledge, all other solutions relying on the cosmological constant do so by initially ad hoc inserting it into Einstein’s field equation. This clarification unveils the true nature of the cosmological constant, suggesting that it serves as a correction factor for strong gravitational fields, accurately predicting real-world cosmological phenomena only within the extremal solutions of the discussed metrics, all derived strictly from Einstein’s field equation.

Dialectical Thermodynamics’Solution to the Conceptual Imbroglio That Is the Reversible Path

According to the second law of thermodynamics, as currently understood, any given transit of a system along the reversible path proceeds with a total entropy change equal to zero. The fact that this condition is also the identifier of thermodynamic equilibrium, makes each and every point along the reversible path a state of equilibrium, and the reversible path, as expressed by a noted thermodynamic author, “a dense succession of equilibrium states”. The difficulties with these notions are plural. The fact, for example, that systems need to be forced out of equilibrium via the expenditure of work, would make any spontaneous reversible process a consumer of work, this in opposition to common thermodynamic wisdom that makes spontaneous reversible processes the most efficient transformers of work-producing-potential into actual work. The solution to this and other related impasses is provided by Dialectical Thermodynamics via its previously proved notion assigning a negative entropy change to the energy upgrading process represented by the transformation of heat into work. The said solution is here exemplified with the ideal-gas phase isomerization of butane into isobutane.

Positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg-de Vries equations

Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method is used to derive several positon and hybrid solutions for the(2+1)-dimensional complex modified Korteweg–de Vries equations. Based on the zero seed solution, the positon solution and the hybrid solutions of positon and soliton are constructed. The composition of positons is studied, showing that multi-positons of(2+1)-dimensional equations are decomposed into multi-solitons as well as the(1+1)-dimensions. Moreover, the interactions between positon and soliton are analyzed. In addition, the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution, and their evolutions with time are discussed.

Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

Diversity of Rogue Wave Solutions to the (1+1)-Dimensional Boussinesq Equation

A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 but also has a relationship with the other parameters c0, α, β.