Related papers: A new solvable many-body problem of goldfish type
A manifestation of the three-body forces in multiparticle dynamics is discussed. The minireview of our recent results has been presented.
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
The three-body problem, which describes three masses interacting through Newtonian gravity without any restrictions imposed on the initial positions and velocities of these masses, has attracted the attention of many scientists for more…
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
In this paper, we prove that the linearized system of elliptic triangle homographic solution of planar charged three-body problem can be transformed to that of the elliptic equilateral triangle solution of the planar classical three-body…
A new presentation of the $n$-string braid group $B_n$ is studied. Using it, a new solution to the word problem in $B_n$ is obtained which retains most of the desirable features of the Garside-Thurston solution, and at the same time makes…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
The stability issue of a large class of modified gravitational models is discussed with particular emphasis to de Sitter solutions. Three approaches are briefly presented and the generalization to more general cases is mentioned.
This paper deals with bounded solutions of quasilinear elliptic equations on Riemannian manifolds satisfying special condition.
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
Recent progress in the gauge-mediated supersymmetry breaking is reviewed, with emphasis on the theoretical problems which gauge-mediated models so successfully solve, as well as those problems which are endemic to the models themselves and…
A multiple Gauss sum is a complete multiple exponential sum twisted by Dirichlet characters. We prove a new bound for multiple Gauss sums and, as an application, improve previous results in the Birch--Goldbach problem. Let $F_1, \ldots, F_R…
We consider the problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We introduce a new integrable case, valid on zero level of the cyclic integral, that…
We consider the question how well a floating body can be approximated by the polar of the illumination body of the polar. We establish precise convergence results in the case of centrally symmetric polytopes. This leads to a new affine…
It is shown that there exist solutions of the quasipotential equations exhibiting the abnormal type behaviour of the Bethe-Salpeter equation.
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
The existence of stable multiquarks made of heavy quarks and antiquarks is discussed in the framework of potential models. It is stressed that the few-body problem should be handled seriously and accurately. No bound state is found within…
The problem of separation of variables in some coordinate systems obtained with the use of $L$-transformations is studied. Potentials are shown that allow separation of regular variables in a perturbed two-body problem. The potential…
We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.
In this work, we introduce a novel approach for solving tridiagonal Toeplitz systems with multiple right-hand sides.